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  • 1
    Electronic Resource
    Electronic Resource
    Masthead (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090101
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  • 2
    Electronic Resource
    Electronic Resource
    Momentum transport in a turbulent mixing layer (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 23-41 
    Details
    ISSN: 0271-2091
    Keywords: Momentum transport ; Turbulent mixing layers ; Discrete vortex method ; Time-dependent momentum fluctuations ; Comparison with experiments ; Large-scale structures ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The turbulent momentum transport phenomena in a two-dimensional mixing layer are investigated numerically by a discrete vortex method. The numerical model and calculations are verified through a comparison with existing numerical simulations and experimental measurements. The main emphasis is placed on the exploration of the detailed time-dependent instantaneous local momentum fluctuations and on the comparison of numerical results with available experimental measurements. The current simulations confirm qualitatively the various trends in the turbulent momentum flux and fluctuating components of the velocity in the mixing layer found with several experimental results. The study shows that similarity exists in turbulent momentum quantities along the axial direction of the mixing layer. The calculations also show a definite correlation between the passage of a large-scale structure and a burst in the turbulent momentum flux. The probability density functions of the fluctuating quantities are shown to be mostly Gaussian-like, with only a few exceptions.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090104
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  • 3
    Electronic Resource
    Electronic Resource
    Are fem solutions of incompressible flows really incompressible? (or how simple flows can cause headaches!) (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 99-112 
    Details
    ISSN: 0271-2091
    Keywords: Mixed and penalty FEM ; Navier-Stokes equations ; Round-off and ill conditioning ; Pressure discretization ; Coupled flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: It is generally accepted that mixed and penalty finite element methods can routinely solve the incompressible Navier-Stokes equations. This paper shows by means of simple examples that problems can arise even for the simpler Stokes equations. The causes of the problem fall in either of two categories: round-off and ill conditioning, or a poor choice of pressure discretization. Nonsensical solutions can be obtained. Computation of the discrete divergence of the flow field is a simple and powerful tool to diagnose such conditions. In the first part of the paper several simple techniques for minimizing the effect of round-off are reviewed. In the second part it is shown that, for coupled flow problems, care must be exercised in the choice of the pressure approximation. A unified treatment of various observations by different workers is presented. This should prove useful for general users of the finite element method.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090108
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  • 4
    Electronic Resource
    Electronic Resource
    Euler flow solutions for transonic shock wave-boundary layer interaction (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 59-73 
    Details
    ISSN: 0271-2091
    Keywords: Steady Euler equations ; Transonic flows ; Multigrid methods ; Boundary conditions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Steady 2D Euler flow computations have been performed for a wind tunnel section, designed for research on transonic shock wave-boundary layer interaction. For the discretization of the steady Euler equations, an upwind finite volume technique has been applied. The solution method used is collective, symmetric point Gauss-Seidel relaxation, accelerated by non-linear multigrid. Initial finest grid solutions have been obtained by nested iteration. Automatic grid adaptation has been applied for obtaining sharp shocks. An indication is given of the mathematical quality of four different boundary conditions for the outlet flow. Two transonic flow solutions with shock are presented: a choked and a non-choked flow. Both flow solutions show good shock capturing. A comparison is made with experimental results.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090106
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  • 5
    Electronic Resource
    Electronic Resource
    Numerical simulation of axisymmetric turbulent flow in combustors and diffusers (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 167-183 
    Details
    ISSN: 0271-2091
    Keywords: Axisymmetric turbulent flow ; Combustors ; Diffusers ; Navier-Stokes equations k-∊ model ; Zonal grid ; Finite differences ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical studies of turbulent flow in an axisymmetric 45° expansion combustor and bifurcated diffuser are presented. The Navier-Stokes equations incorporating a k-∊ model were solved in a non-orthogonal curvillinear co-ordinate system. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite differencing methods - hybrid, quadratic upwind and skew upwind - were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090204
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  • 6
    Electronic Resource
    Electronic Resource
    Conjugate gradient methods and ILU preconditioning of non-symmetric matrix systems with arbitrary sparsity patterns (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 213-233 
    Details
    ISSN: 0271-2091
    Keywords: Preconditioning ; Conjugate gradients ; Non-symmetric matrices ; Finite elements ; Convective transport ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Preconditioning techniques based on incomplete Gaussian elimination for large, sparse, non-symmetric matrix systems are described. A certain level of fill-in may be specified in the incomplete factorizations. All methods considered may be applied to matrices with arbitrary sparsity patterns, for instance those associated with the general preprocessor algorithms or adaptive mesh techniques. The preconditioners have been combined with five conjugate gradient-like methods and tested on finite element discretized scalar convection-diffusion equations in 2D and 3D. It is found from numerical experiments that an amount of fill-in corresponding to about 50% of the number of original non-zero matrix entries is the optimal choice for this class of preconditioners. The preconditioners show almost no sensitivity to grid distortion. In problems with significantly variable coefficients or anisotropy the preconditioners stabilize the basic iterative schemes in addition to reducing the computational work substantially, mostly by more than 90%. The modified preconditioning technique, where fill-in is added on the main diagonal, performs in general better than the standard incomplete LU factorization, but is inferior to the latter in 3D problems and for matrix systems with complicated sparsity patterns.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090207
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  • 7
    Electronic Resource
    Electronic Resource
    Announcement (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 374-374 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090311
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  • 8
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    A Chebyshev collocation method for the Navier-Stokes equations with application to double-diffusive convection (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 427-452 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Spectral method ; Chebyshev polynomials ; Convection ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A Chebyshev collocation method for solving the unsteady two-dimensional Navier-Stokes equations in vorticity-streamfunction variables is presented and discussed. The discretization in time is obtained through a class of semi-implicit finite difference schemes. Thus at each time cycle the problem reduces to a Stokes-type problem which is solved by means of the influence matrix technique leading to the solution of Helmholtz-type equations with Dirichlet boundary conditions. Theoretical results on the stability of the method are given. Then a matrix diagonalization procedure for solving the algebraic system resulting from the Chebyshev collocation approximation of the Helmholtz equation is developed and its accuracy is tested. Numerical results are given for the Stokes and the Navier-Stokes equations. Finally the method is applied to a double-diffusive convection problem concerning the stability of a fluid stratified by salinity and heated from below.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090405
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  • 9
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    Robust semidirect finite difference methods for solving the Navier-Stokes and energy equations (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 325-340 
    Details
    ISSN: 0271-2091
    Keywords: Semidirect methods ; Finite difference formulation ; Robust solutions ; Navier-Stokes and energy equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Semidirect solution techniques can be an effective alternative to the more conventional iterative approaches used in many finite difference methods. This paper summarizes several semidirect techniques which generally have not been applied to the Navier-Stokes and energy equations in finite difference form. The methods presented use both successive substitution and Jacobian-based updates as well as two variations of Broyden's full matrix update. A hybrid method is also presented, as is a norm-reducing search technique that can be used to enhance the convergence characteristics of any semidirect approach. These methods have been compared with the well known iterative methods SIMPLE and SIMPLER. The comparison was performed on the natural convection and driven cavity problems. The semidirect methods proved to be reliably convergent without the need for a priori specification of variable under-relaxation factors, which was necessary with the iterative methods. Natural convection and driven cavity solutions have been readily obtained with the proposed methods for Rayleigh and Reynolds numbers up to 109 and 106 respectively. Of the semidirect techniques, the hybrid approach was the most robust. From an arbitrary zero initial guess this method was able to obtain a solution to the natural convection problem for Rayleigh numbers three orders of magnitude larger than was possible with the Newton-Raphson update. The computational effort required by the semidirect methods is comparable to that required by the iterative methods; however, the memory requirements can be significantly greater.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090307
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  • 10
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1051-1055 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090810
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  • 11
    Electronic Resource
    Electronic Resource
    Finite element technique to solve the elastic strain for Leonov fluid flow (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1059-1072 
    Details
    ISSN: 0271-2091
    Keywords: Viscoelastic flow ; Leonov model ; Convective integration ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The finite element method is used to find the elastic strain (and thus the stress) for given velocity fields of the Leonov model fluid. With a simple linearization technique and the Galerkin formulation, the quasi-linear coupled first-order hyperbolic differential equations together with a non-linear equality constraint are solved over the entire domain based on a weighted residual scheme. The proposed numerical scheme has yielded efficient and accurate convective integrations for both the planar channel and the diverging radial flows for the Leonov model fluid. Only the strain in the inflow plane is required to be prescribed as the boundary conditions. In application, it can be conveniently incorporated in an existing finite element algorithm to simulate the Leonov viscoelastic fluid flow with more complex geometry in which the velocity field is not known a priori and an iterative procedure is needed.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090902
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  • 12
    Electronic Resource
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 741-745 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090607
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  • 13
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    A Newton/upwind method and numerical study of shock wave/boundary layer interactions (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 747-761 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes solutions ; Shock wave/boundary layer interactions ; Newton's iteration ; Upwind differencings ; Symmetric line relaxation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The objective of the paper is twofold. First we describe an upwind/central differencing method for solving the steady Navier-Stokes equations. The symmetric line relaxation method is used to solve the resulting algebraic system to achieve high computational efficiency. The grid spacings used in the calculations are determined from the triple-deck theory, in terms of Mach and Reynolds numbers and other flow parameters. Thus the accuracy of the numerical solutions is improved by comparing them with experimental, analytical and other computational results. Secondly we proceed to study numerically the shock wave/boundary layer interactions in detail, with special attention given to the flow separation. The concept of free interaction is confirmed. Although the separated region varies with Mach and Reynolds numbers, we find that the transverse velocity component behind the incident shock, which has not been identified heretofore, is also an important parameter. A small change of this quantity is sufficient to eliminate the flow separation entirely.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090702
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  • 14
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 865-869 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090708
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  • 15
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    Numerical simulation and hydrodynamic visualization of transient viscous flow around an oscillating aerofoil (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 891-920 
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    ISSN: 0271-2091
    Keywords: Transient flows ; Oscillating aerofoil ; Dynamic stall ; Navier-Stokes equations ; Finite differences ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Unsteady viscous flow around a large-amplitude and high-frequency oscillating aerofoil is examined in this paper by numerical simulation and experimental visualization. The numerical method is based on the combination of a fourth-order Hermitian finite difference scheme for the stream function equation and a classical second-order scheme to solve the vorticity transport equation. Experiments are carried out by a traditional visualization method using solid tracers suspended in water. The comparison between numerical and experimental results is found to be satisfactory. Time evolutions of the flow structure are presented for Reynolds numbers of 3 × 103 and 104. The influence of the amplitude and frequency of the oscillating motion on the dynamic stall is analysed.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090803
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  • 16
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    Comments on a recent paper by W. Zijl (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1302-1304 
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    ISSN: 0271-2091
    Keywords: Incompressible flow ; Clebsch potentials ; Three-dimensional ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A recent paper by W. Zijl, which reformulated the Navier-Stokes and Boussinesq equations in terms of Clebsch potentials, has an error that greatly reduces the generality of the results. Some other recent efforts to use such potentials in fluid and plasma dynamics are briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091010
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  • 17
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    Comment on ‘generalized potential flow theory and direct calculation of velocities applied to the numerical solution of the Navier-Stokes and the Boussinesq equations’ (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1299-1301 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In a recent paper a generalized potential flow theory and its application to the solution of the Navier-Stokes equation are developed.1 The purpose of this comment is to show that the analysis presented in that paper is in general not correct. We note that the theoretical development of Reference 1 is in fact an extension - although not cited - of some work first done by Hawthorne for steady inviscid flow.2 Hawthorne's solution is correct, and his analysis, which we briefly describe, provides a useful introduction to this note.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091009
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  • 18
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    Numerical studies of slow viscous rotating flow past a sphere. II (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1307-1319 
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    ISSN: 0271-2091
    Keywords: Peaceman-Rachford ADI method ; SOR method ; Oseen approximation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Navier-Stokes equations, which are the governing equations for a steady, viscous, incompressible fluid rotating about the z-axis with angular velocity ω, are linearized using the Oseen approximation. Two parameters, namely the Reynolds number Re = Ua/v and Reω = 2ωa2/v (the Reynolds number w.r.t. rotation), enter the linearized equations. These equations are solved by the Peaceman-Rachford ADI method and the resulting algebraic equations are solved by the SOR method. Streamlines are plotted and compared with the Oseen solution for the non-rotating case. The magnitude of the vorticity vector with increasing θ is also plotted.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650091102
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  • 19
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    A numerical study of heat and momentum transfer for tube bundles in crossflow (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1381-1394 
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    ISSN: 0271-2091
    Keywords: Heat exchangers ; Crossflow ; Tube bundle ; Nusselt number ; Streamfunction/vorticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical scheme is developed to predict the heat transfer and pressure drop coefficients in flow through rigid tube bundles. The scheme uses the Galerkin finite element technique. The conservation equations for laminar steady-state flow are cast in the form of streamfunction and vorticity equations. A Picard iteration method is used for the solution of the resulting system of non-linear algebraic equations. Results for the heat transfer and pressure drop coefficients are obtained for tube arrays of pitch ratios of 1·5 and 2·0. Very good agreement of the present results and experimental data obtained in the past is observed up to Reynolds numbers of 1000. It is also observed that the results of the present method show better agreement with the experimental data and that they are applicable for higher Reynolds numbers than results of other studies.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650091107
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  • 20
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    An efficient algorithm for compressible flows with real gases (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1269-1283 
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    ISSN: 0271-2091
    Keywords: Euler equations ; Real gases ; Local parametrization of the equation of state ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An efficient algorithm is presented for the solution of the Euler equations of gas dynamics with a general convex equation of state. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only one function evaluation in each computational cell is required by using a local parametrization of the equation of state. The scheme is applied to two standard test problems in gas dynamics for some specimen equations of state.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091007
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  • 21
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    The simple layer potential method of fundamental solutions for certain biharmonic problems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1221-1234 
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    ISSN: 0271-2091
    Keywords: Biharmonic equation ; Stokes flow ; Simple layer potential ; Method of fundamental solutions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A novel formulation of the method of fundamental solutions for the numerical solution of plane biharmonic problems, based on the simple layer potential representation of Fichera, is presented. The applicability and accuracy of the method are demonstrated by examining its performance on a set of practical problems arising in Stokes fluid flow.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650091005
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  • 22
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    A finite element analysis of laminar unsteady flow of viscoelastic fluids through channels with non-uniform cross-sections (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1487-1501 
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    ISSN: 0271-2091
    Keywords: Viscoelastic fluid ; Polymer flow ; Velocity correction method ; Two-step explicit scheme ; Pressure boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The effects of non-Newtonian behaviour of a fluid and unsteadiness on flow in a channel with non-uniform cross-section have been investigated. The rheological behaviour of the fluid is assumed to be described by the constitutive equation of a viscoelastic fluid obeying the Oldroyd-B model. The finite element method is used to analyse the flow. The novel features of the present method are the adoption of the velocity correction technique for the momentum equations and of the two-step explicit scheme for the extra stress equations. This approach makes the computational scheme simple in algorithmic structure, which therefore implies that the present technique is capable of handling large-scale problems. The scheme is completed by the introduction of balancing tensor diffusivity (wherever necessary) in the momentum equations. It is important to mention that the proper boundary condition for pressure (at the outlet) has been developed to solve the pressure Poisson equation, and then the results for velocity, pressure and extra stress fields have been computed for different values of the Weissenberg number, viscosity due to elasticity, etc. Finally, it is pertinent to point out that the present numerical scheme, along with the proper boundary condition for pressure developed here, demonstrates its versatility and suitability for analysing the unsteady flow of viscoelastic fluid through a channel with non-uniform cross-section.
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    URL: http://dx.doi.org/10.1002/fld.1650091205
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  • 23
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1539-1542 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091208
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    Trefftz method for hydrodynamic pressure on rigid dams with non-vertical upstream face (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1-7 
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    ISSN: 0271-2091
    Keywords: Trefftz method ; Hydrodynamic pressure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Based on a two-dimensional potential flow theory, earthquake-induced hydrodynamic pressures on a rigid dam with a non-vertical upstream face are examined by the Trefftz method. The effect of surface waves on the hydrodynamic pressure distribution is discussed in detail. Numerical values are given for different wave effect parameters and different geometries of the dam-water interface.
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    URL: http://dx.doi.org/10.1002/fld.1650090102
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    Velocity-pressure integrated versus penalty finite element methods for high-Reynolds-number flows (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 43-57 
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    ISSN: 0271-2091
    Keywords: Finite element ; Penalty method ; Consistent penalty ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Velocity-pressure integrated and consistent penalty finite element computations of high-Reynolds-number laminar flows are presented. In both methods the pressure has been interpolated using linear shape functions for a triangular element which is contained inside the biquadratic flow element. It has been shown previously that the pressure interpolation method, when used in conjunction with the velocity-pressure integrated method, yields accurate computational results for high-Reynolds-number flows. It is shown in this paper that use of the same pressure interpolation method in the consistent penalty finite element method yields computational results which are comparable to those of the velocity-pressure integrated method for both the velocity and the pressure fields. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine grid finite difference computational results. Advantages and disadvantages of the two finite element methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow of Reynolds number 10 000, a laminar backward-facing step flow and a laminar flow through a nest of cylinders.
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    URL: http://dx.doi.org/10.1002/fld.1650090105
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    Finite difference methods for solving the two-dimensional advection-diffusion equation (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 75-98 
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    ISSN: 0271-2091
    Keywords: 2D Advection-diffusion equation ; Finite difference method ; Weighted discretization ; Modified equivalent PDE approach ; Stability ; Accuracy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Using weighted discretization with the modified equivalent partial differential equation approach, several accurate finite difference methods are developed to solve the two-dimensional advection-diffusion equation following the success of its application to the one-dimensional case. These new methods are compared with the conventional finite difference methods in terms of stability and accuracy. The new methods are more accurate and often more stable than the conventional schemes.
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    URL: http://dx.doi.org/10.1002/fld.1650090107
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    Announcements (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 125-125 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090111
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    Numerical analysis of the developing fluid flow in a circular duct rotating steadily about a parallel axis (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 151-165 
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    ISSN: 0271-2091
    Keywords: Numerical analysis ; Fluid flow ; Rotating circular duct ; Finite cell method ; Finite element method ; Swirl ; Inlet boundary conditions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical analysis of the flow pattern in the inlet region of a circular pipe rotating steadily about an axis parallel to its own is presented. Both finite cell and finite element methods are used to analyse the problem and they give qualitatively similar results which show that a swirling fluid motion is induced in the pipe inlet region. The analyses show that the direction of swirl is opposite to that of the pipe rotation when viewed along the flow axis and that its magnitude depends on the speed of pipe rotation and throughflow Reynolds number. Neither numerical analysis predicts the marked upturn in friction factor (or pressure drop) which has been observed experimentally. However, a dependence on the pipe inlet boundary conditions is demonstrated.
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    URL: http://dx.doi.org/10.1002/fld.1650090203
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 245-249 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090209
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    Process splitting of the boundary conditions for the advection-dispersion equation (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 235-244 
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    ISSN: 0271-2091
    Keywords: Process splitting ; Advection-dispersion equation ; Boundary conditions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Rational strategies are considered for the specification of the intermediate boundary condition at an inflow boundary where process splitting (fractional steps) is adopted in solving the advection-dispersion equation. Three lowest-order methods are initially considered and evaluation is based on comparisons with an analytical solution. For flow and dispersion parameter ranges typical of rivers and estuaries, the given boundary condition for the complete advection-dispersion equation at the end of the complete time step provides a satisfactory estimate of the intermediate boundary value. This was further confirmed by the development and evaluation of two higher-order methods. These required non-centred discrete approximations for spatial derivatives, which offset any special advantages from the higher truncation error order.
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    Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady euler equations (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 305-323 
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    ISSN: 0271-2091
    Keywords: Steady Euler equations ; Variational method ; 3D vortex flows ; Finite element approximation ; Newton linearization ; Least-squares formulation ; Subsonic and supersonic flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A variational method for solving directly the full steady Euler equations is presented. This method is based on both Newton's linearization and a least squares formulation. The validity of the Euler model and boundary conditions to capture the vortex sheet is discussed. A finite element approximation of the groups of conservative variables is described and results are given for 3D subsonic flows as well as supersonic flows past a flat plate at high angle of attack.
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    URL: http://dx.doi.org/10.1002/fld.1650090306
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    Numerical simulation of silencers (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 363-368 
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    ISSN: 0271-2091
    Keywords: Silencers ; Noise attenuation ; Shock flow ; Numerical simulation ; Gas dynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The problem of attenuating the noise from weapons firing is studied experimentally and numerically. As a possible method of attenuating the noise significantly, a silencer with no internal baffles is attached to the M242 cannon. The internal pressures inside the muffler are measured. The near-field overpressures outside the muffler at various polar angles are also measured. A numerical simulation of the flow through the muffler is performed, using Harten's shock-capturing method to solve the Euler equations of ideal compressible flow. The numerical simulation yields a detailed picture of the flow field as displayed by the pressure and Mach contours. Pressure-time curves at selected locations are obtained and compared with experimental data. There is good agreement, except that the numerical simulation generates more vigorous oscillations.
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    URL: http://dx.doi.org/10.1002/fld.1650090309
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    Radiative transfer to oscillatory hydromagnetic rotating flow of a rarefied gas past a horizontal flat plate (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 375-384 
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    ISSN: 0271-2091
    Keywords: Hydromagnetic ; Radiating ; Rarefied gas flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Hydromagnetic flow past an infinite horizontal plate is considered when the flow is rarefied and the temperature of the wall is high enough for radiative heat transfer to be significant. In the undisturbed flow far away from the plate, an oscillatory velocity is superimposed on a steady mean and the whole configuration is in constant rotation. When the flow is slightly rarefied, the compressible Navier-Stokes equations and the slip boundary conditions together with the general differential approximation for radiation suffice for the analytical description of the problem. If the amplitude of oscillation is small, the problem is tackled by a perturbation scheme and numerical integration. Consequences of the effect of rotation and oscillation on the flow variables are discussed.
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 493-497 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090407
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    Flame computations by a Chebyshev multidomain method (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 499-515 
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    ISSN: 0271-2091
    Keywords: Chebyshev collocation ; Laminar flames ; Domain decomposition ; Influence matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A Chebyshev collocation method is proposed for the computation of laminar flame propagation in a two-dimensional gaseous medium. The method is based on a domain decomposition technique associated with co-ordinate transforms to map the infinite physical subdomains into finite computational ones. The influence matrix method is used to handle the patching conditions at the interfaces. This technique is particularly efficient since at each time step only matrix products have to be performed. The method is tested first on an elliptic model problem; it is then applied to laminar flame computations, including calculations of cellular instabilities of flame fronts.
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    A pressure-smoothing scheme for incompressible flow problems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 557-567 
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    ISSN: 0271-2091
    Keywords: Pressure-smoothing scheme ; Least square ; Finite element method ; Incompressible flow ; Newtonian and Maxwell fluids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A pressure-smoothing scheme for Stokes and Navier-Stokes flows of Newtonian fluids and for Stokes flow of Maxwell fluids is described. The stress deviator obtained from the calculated velocity field is substituted into the governing equilibrium equation. The resulting equation is then solved to obtain a new, smoothed pressure by a least square finite element method.
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    URL: http://dx.doi.org/10.1002/fld.1650090506
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 619-622 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090511
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    Quantum phenomena in numerical wave propagation (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 623-650 
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    ISSN: 0271-2091
    Keywords: Numerical analysis ; Wave propagation ; Hyperbolic equations ; Quantum mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The analysis of wave propagation in computing domains where hyperbolic equations are approximated with finite differences has revealed surprising analogies between this subject and quantum mechanics. The first part of this paper consists of a review of the corresponding phenomena and of their description with known results from numerical analysis and wave propagation theory. We then introduce a new formalism, containing a finite difference analogue of the classical Schrodinger equation, which describes the ensemble of those phenomena. The validity of the new formalism is verified by its agreement with known theoretical results in numerical wave propagation (it contains in fact many of those results) as well as with new data obtained in numerical experiments with monochromatic waves which display properties similar to those of Schrödinger's wavefunction for the quantum mechanics description of the equivalent experiments with physical particles. While the results of this paper are derived in the context of wave propagation in computing domains, they remain applicable to similar aspects of wave propagation in other (physical) periodic structures.
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    Coupled heat transfer and viscous flow, and magnetic effects in weld pool analysis (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 713-730 
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    ISSN: 0271-2091
    Keywords: Viscous flow ; Heat transfer ; Phase change ; Finite elements ; Magnetic field ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element formulation and analysis is developed to study coupled heat transfer and viscous flow in a weld pool. The thermal effects generate not only buoyancy forces but also a variation in the surface tension which acts to drive the viscous flow in the molten weld pool. A moving phase boundary separates molten and solid material. Numerical experiments reveal the nature of the highly convective flow in the weld pool and the associated thermal profiles. The relative importance of buoyancy, surface tension, phase change, convection, etc. are examined. We also consider the sensitivity of the solution to the finite element mesh and related non-linear numerical instabilities. Of particular interest is the coupling of the thermal and viscous flow fields for the case when radial flow is inward or outward.
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    Multifronts and transputer networks for solving fluid mechanical finite element systems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 731-740 
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    ISSN: 0271-2091
    Keywords: Multifrontal solver ; Transputer networks ; Fluid mechanics ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with the implementation of a multifrontal solver on a network of transputers. We briefly discuss the transputer, outline the frontal and multifrontal schemes and consider the implementation of these schemes on the network. Results are presented for two test problems in fluid mechanics showing that the solver displays close to linear speed-up.
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    A total pressure correction for upstream weighted schemes (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 855-864 
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    ISSN: 0271-2091
    Keywords: Finite volume method ; Accurate total pressure prediction ; Discretization accuracy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Upwind differencing is known to lead to a substantial loss in total pressure. The present paper illustrates the importance of this error on two problems: flow in a converging-diverging duct and flow around a cylinder. A correction is proposed that reduces the total pressure error and yields dramatically improved results for the test problems.
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    Navier-Stokes computation of transonic vortices over a round leading edge delta wing (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 943-962 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes solver ; Vortex motion ; Finite volume method ; Viscous flow ; Delta wing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A 3D Navier-Stokes solver has been developed to simulate laminar compressible flow over quadrilateral wings. The finite volume technique is employed for spatial discretization with a novel variant for the viscous fluxes. An explicit three-stage Runge-Kutta scheme is used for time integration, taking local time steps according to the linear stability condition derived for application to the Navier-Stokes equations. The code is applied to compute primary and secondary separation vortices at transonic speeds over a 65° swept delta wing with round leading edges and cropped tips. The results are compared with experimental data and Euler solutions, and Reynolds number effects are investigated.
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    An investigation of pressure transients in pipelines with two-phase bubbly flow (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1207-1219 
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    ISSN: 0271-2091
    Keywords: Centre implicit method ; Pressure transients ; Two-phase pipe flow ; Bubbly pipe flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a two-dimensional model for the analysis of the pressure transient of a two-phase homogeneous bubbly mixture flowing in a pipeline and the numerical integration using the centre implicit method (CIM). Experiments were conducted to confirm the proposed sonic speed equation of an air-water mixture for an air concentration of less than 1%. The 2D CIM model is compared with the method of characteristics (MoC) for a two-phase bubbly flow in a pipeline. The comparisons show that the proposed 2D CIM model generally gives good agreement with the method of characteristics.
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    Second-moment closure and its use in modelling turbulent industrial flows (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 963-985 
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    ISSN: 0271-2091
    Keywords: Second moment ; Turbulence ; Transport equations ; Reynolds stress ; Complex flows ; Industrial applications ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Second-moment turbulence models focus directly on the transport equations for the Reynolds stresses rather than supposing the stress and strain fields to be directly linked via an eddy viscosity. This elaboration enables the effects of complex strains and force fields on the turbulence structure to be better captured. The paper summarizes the principal modelling strategies adopted for the unknown processes in these equations and presents the forms that have been found most useful in engineering calculations. Methods adopted for overcoming significant problems of numerical instability and lack of convergence compared with eddy-viscosity-based schemes are also presented. Applications involving momentum and heat transfer in complex flows are drawn from the advanced technology sectors of the power generation and aircraft industries.
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    Announcements (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1057-1057 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    URL: http://dx.doi.org/10.1002/fld.1650090811
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    Three-dimensional reduced Navier-Stokes solutions for subsonic separated and non-separated flows, using a global pressure relaxation procedure (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1087-1098 
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    ISSN: 0271-2091
    Keywords: RNS ; Separation ; Direct solver ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The reduced Navier-Stokes and thin layer approximations to the Navier-Stokes equations are used to obtain solutions for viscous subsonic three-dimensional flows. A spatial marching method is combined with a direct sparse matrix solver to obtain successive solutions in a global relaxation process. Results have been obtained for flow fields with and without regions of flow reversal.
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    A velocity formulation for flow past a symmetric profile with a wake (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1113-1119 
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    ISSN: 0271-2091
    Keywords: Finite element ; Free streamlines ; Wakes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A model having velocity components as basic unknowns is presented for calculation of two-dimensional flow past a symmetric profile with a wake in a channel. A modified least squares functional is used for the finite element solution of velocities. The determination of the position of the free streamline is treated as an optimum design problem. The concepts of cost function, geometry parameter and sensitivity derivative are employed. Numerical results are compared with published results obtained with streamfunction formulations.
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1179-1182 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090910
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    Numerical solution of transonic flows on a streamfunction co-ordinate system (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1183-1193 
    Details
    ISSN: 0271-2091
    Keywords: CFD ; Transonics ; Streamfunction co-ordinates ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new method has been developed for the computation of steady two-dimensional full-potential transonic flow past symmetric aerofoils. This method utilizes von Mises variables (x, ψ), where ψ is taken as the streamfunction for the flow. The flow equations and appropriate boundary conditions are formulated in terms of the von Mises variables (x, ψ) for symmetric aerofoils at zero incidence. This yields a system of two equations for unknowns ρ(x, ψ) and y(x, ψ). Finite difference solutions have been computed using SLOR at subcritical and supercritical Mach numbers. The results are compared with available data and are in excellent agreement.
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    URL: http://dx.doi.org/10.1002/fld.1650091002
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    Internal wave reflections and transmissions arising from a non-uniform mesh. Part III: The occurrence of evanescent waves in the Crank-Nicolson linear finite element scheme (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 833-853 
    Details
    ISSN: 0271-2091
    Keywords: Fourier analysis ; Dispersion relation ; Reflected/transmitted evanescent waves ; Crank-Nicolson linear finite element scheme ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The numerical scheme upon which this paper is based is the 1D Crank-Nicolson linear finite element scheme. In Part I of this series it was shown that for a certain range of incident wavelengths impinging on the interface of an expansion in nodal spacing, an evanescent (or spatially damped) wave results in the downstream region. Here in Part III an analysis is carried out to predict the wavelength and the spatial rate of damping for this wave. The results of the analysis are verified quantitatively with seven ‘hot-start’ numerical experiments and qualitatively with seven ‘cold-start’ experiments. Weare has shown that evanescent waves occur whenever the frequency of a disturbance at a boundary exceeds the maximum frequency given by the dispersion relation. In these circumstances the ‘extended dispersion’ relation can be used to determine the rate of spatial decay.In the context of a domain consisting of two regions with different nodal spacings, the use of the group velocity concept shows that evanescent waves have no energy flux associated with them when energy is conserved.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650090706
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    The development of advanced computational methods for turbomachinery blade design (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 921-941 
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    ISSN: 0271-2091
    Keywords: Blade design ; Compressors ; Turbines ; Navier-Stokes ; Quasi-3D and 3D systems ; Through-flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper describes the basic components of a turbomachinery blade design system in use within Rolls-Royce. A number of modelling aspects of the advanced computational methods in use and under development are reviewed together with areas for future research and development.A quasi-3D blade design system which is used for both compressors and turbines is described covering through-flow and blade-to-blade analysis. Various features of blade-to-blade analysis are discussed including the use of compatible design and analysis modes and coupled boundary layer analysis capable of handling attached and separated flow; examples are included to show capabilities. Advances being made in the development and application of Reynolds-averaged Navier-Stokes models are covered showing capabilities with regard to loss and heat transfer prediction.A fully coupled quasi-3D through-flow and blade-to-blade analysis system is described and results presented to show basic capabilities.The need for 3D flow analysis is discussed and the elements of a 3D blade design system presented showing how this links to the traditional quasi-3D system. Examples are given showing basic capabilities of the methods available and under development.Finally areas for future development are presented indicating the mathematical and numerical modelling problems to be addressed.
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    URL: http://dx.doi.org/10.1002/fld.1650090804
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    Numerical perturbation method for approximate solution of poisson's equation on a moderately deforming grid (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 599-607 
    Details
    ISSN: 0271-2091
    Keywords: Numerical solution of Poisson's equation ; Unsteady incompressible flow ; Moving boundaries ; Numerical solution of partial differential equations ; Numerical perturbation method ; Deforming grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In problems such as the computation of incompressible flows with moving boundaries, it may be necessary to solve Poisson's equation on a large sequence of related grids. In this paper the LU decomposition of the matrix A0 representing Poisson's equation discretized on one grid is used to efficiently obtain an approximate solution on a perturbation of that grid. Instead of doing an LU decomposition of the new matrix A, the RHS is perturbed by a Taylor expansion of A-1 about A0. Each term in the resulting series requires one ‘backsolve’ using the original LU.Tests using Laplace's equation on a square/rectangle deformation look promising; three and seven correction terms for deformations of 20% and 40% respectively yielded better than 1% accuracy.As another test, Poisson's equation was solved in an ellipse (fully developed flow in a duct) of aspect ratio 2/3 by perturbing about a circle; one correction term yielded better than 1% accuracy.Envisioned applications other than the computation of unsteady incompressible flow include: three-dimensional parabolic problems in tubes of varying cross-section, use of ‘elimination’ techniques other than LU decomposition, and the solution of PDEs other than Poisson's equation.
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    URL: http://dx.doi.org/10.1002/fld.1650090509
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    Algebraic turbulence models for the computation of two-dimensional high-speed flows using unstructured grids (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1121-1143 
    Details
    ISSN: 0271-2091
    Keywords: Turbulence ; High-speed flows ; Unstructured grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The incorporation of algebraic turbulence models in a solver for the 2D compressible Navier-Stokes equations using triangular grids is described. A practical way to use the Cebeci-Smith model and to modify it in separated regions is proposed. The ability of the model to predict high-speed perfect-gas boundary layers is investigated from a numerical point of view.
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    URL: http://dx.doi.org/10.1002/fld.1650090907
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    Stable second-order accurate iterative solutions for second-order elliptic problems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 583-598 
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    ISSN: 0271-2091
    Keywords: Upwind ; Second order ; Stable schemes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper describes a numerical scheme for solving a convection-diffusion elliptic system with very small diffusion coefficients. This iterative numerical procedure is unconditionally stable and converges very rapidly. Although only linear equations are considered here, this technique can be easily extended to non-linear equations, while keeping its main features as for the linear case. The numerical experiments presented are quite general and confirm most of these features. These examples also show a good way of implementing this scheme.
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    URL: http://dx.doi.org/10.1002/fld.1650090508
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    Masthead (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090601
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    Numerical study of the axially symmetric motion of an incompressible viscous fluid in an annulus between two concentric rotating spheres (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 689-712 
    Details
    ISSN: 0271-2091
    Keywords: Rotating spheres ; Viscous flow ; Incompressible fluid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The research reported herein involved the study of the transient motion of a system consisting of an incompressible Newtonian fluid in an annulus between two concentric, rotating, rigid spheres. The primary purpose of the research was to study the use of a numerical method for analysing the transient motion that results from the interaction between the fluid in the annulus and the spheres which are started suddenly by the action of prescribed torques. The problems considered in this research included cases where: (a) one or both spheres rotate with prescribed constant angular velocities and (b) one sphere rotates due to the action of an applied constant or impulsive t̰orque.In this research the coupled solid and fluid equations were solved numerically by employing the finite difference technique. With the approach adopted in this research, only the derivatives with respect to spatial variables were approximated with the use of the finite difference formulae. The steady state problem was also solved as a separate problem (for verification purposes), and the results were compared with those obtained from the solution of the transient problem. Newton's algorithm was employed to solve the algebraic equations which resulted from the steady state problem, and the Adams fourth-order predictor-corrector method was employed to solve the ordinary differential equations for the transient problem. Results were obtained for the streamfunction, circumferential function, angular velocity of the spheres and viscous torques acting on the spheres as a function of time for various values of the system dimensionless parameters.
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    URL: http://dx.doi.org/10.1002/fld.1650090604
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    Suppression of irregular frequency effects in fluid-structure interaction problems using a combined boundary integral equation method (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 763-782 
    Details
    ISSN: 0271-2091
    Keywords: Combined boundary integral equation method ; Fluid-structure interaction ; Irregular frequencies ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: It is well known that at certain discrete frequencies the conventional boundary integral equation formulation of free surface fluid-structure interaction analyses breaks down. At such ‘irregular’ frequencies the BIE method fails to provide either an acceptable or a unique solution. Having established the existence of irregular frequencies, a review of the different approaches adopted to remedy this problem is presented.A very simple modification of the BIE method is also presented to eliminate the irregular frequency problem. The proposed procedure, designated the combined boundary integral equation method (CBIEM), can be categorized as a modified integral domain method. A description of the CBIEM formulation is presented and its ability to provide a unique solution at all frequencies is demonstrated. Predictions of 3D hydrodynamic reactive coefficients of added mass and fluid damping for a Series 60 hull form and an ellipsoid based on the CBIEM procedure are presented. These predictions are compared with results generated using conventional integral equation methods. The numerical studies demonstrate that the CBIEM is both a practical and effective method of suppressing irregular frequencies. In particular, the procedure is easy to implement in existing BIE computer codes with minimal additional computational effort.
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    Two-dimensional subcritical and supercritical open channel flow calculation using a time-marching method (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1331-1352 
    Details
    ISSN: 0271-2091
    Keywords: Finite volume ; Time-marching ; High-speed free-surface flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A time-marching method is presented for the calculation of two-dimensional, high-speed channel flow, including the usually neglected terms of slope and bottom friction. Time-marching methods are potentially the most flexible means of calculating flow through geometrically complex channel passages, since they can readily deal with subcritical and supercritical flows. The adopted numerical scheme comes straight from gas flow computations in turbomachines. The flow is assumed to be fully mixed in the vertical direction, so that vertical variations may be neglected. Comparisons with other numerical solutions for various open channel configurations show that the proposed approach is a comparatively accurate, reliable and fast technique. It can be utilized for open channel designs.
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    URL: http://dx.doi.org/10.1002/fld.1650091104
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1427-1428 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091110
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    Announcement (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1429-1429 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    URL: http://dx.doi.org/10.1002/fld.1650091111
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    Comparison with experiment for TVD calculations of blast waves from a shock tube (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 9-22 
    Details
    ISSN: 0271-2091
    Keywords: Shock capturing ; Shock tube ; TVD scheme ; Compressible flow ; Fluid dynamics ; Comparison with experiment ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Harten's second-order-accurate total-variation-diminishing (TVD) scheme is applied to calculation of flow from the open end of a shock tube. Comparison of numerical results with available experimental data for overpressure at selected points around the shock tube exit shows good agreement. Numerically indicated positions of the moving shock front and Mach stem also compare well with flow shadowgraph data. Where the problem geometry is sufficiently simple and rectangular gridding can be used, Harten's method affords a good choice for blast wave calculations.
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 121-124 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    URL: http://dx.doi.org/10.1002/fld.1650090110
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    Masthead (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090201
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    Efficient quadrature for a boundary element method to compute three-dimensional Stokes flow (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 185-191 
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    ISSN: 0271-2091
    Keywords: Stokes equations ; Boundary elements ; Quadrature ; Triangular co-ordinates ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A collocation-type boundary element method based on bilinear B-splines is used for the numerical solution of the Stokes Dirichlet problem in bounded domains D ⊂ R3. The computation of the influence matrix requires the numerical evaluation of weakly singular integrals on the domain boundary if the usual double-layer potential ansatz is chosen. Here mostly standard methods with disjoint grids for collocation and integration are used. We develop a special integration scheme based on triangular co-ordinates near the singularity and show its efficiency compared with the method mentioned above.
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    Announcements (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 250-250 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090210
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    A new look at Theodorsen's method in aerofoil theory (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 251-262 
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    ISSN: 0271-2091
    Keywords: Theodorsen's method ; Incompressible flow ; Aerofoil theory ; Thickness ratio ; Camber ratio ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Theodorsen's method for calculating the incompressible potential flow past an aerofoil is viewed afresh. It is found that some simple modifications to the computational process make the computations relatively faster, easier and more accurate. The new modifications are applicable to the analysis of conventional aerofoils with up to moderate thickness and camber ratios. Several examples are presented to show the effectiveness of the modifications.
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    Finite element solution of an enclosed turbulent diffusion flame (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 289-303 
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    ISSN: 0271-2091
    Keywords: Enclosed turbulent diffusion flames ; Finite elements ; Segregated formulation ; κ-∊ turbulence model ; Eddy dissipation concept ; Moment method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element formulation of enclosed turbulent diffusion flames is presented. A primitive variables approach is preferred in the analysis. A mixed interpolation is employed for the velocity and pressure. In the solution of the Navier-Stokes equations, a segregated formulation is adopted, where the pressure discretization equation is obtained directly from the discretized continuity equation, considering the velocity-pressure relationships in the discretized momentum equations. The state of turbulence is defined by a κ-∊ model. Near solid boundaries, a wall function approach is employed. The combustion rates are estimated using the eddy dissipation concept. The expensive direct treatment of the integrodifferential equations of radiation is avoided by employing the moment method, which allows the derivation of an approximate local field equation for the radiation intensity. The proposed finite element model is verified by investigating a technical turbulent diffusion flame of semi-industrial size, and comparing the results with experiments and finite difference predictions.
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    Conference diary (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 369-373 
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    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    URL: http://dx.doi.org/10.1002/fld.1650090310
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    Masthead (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090401
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    A point implicit unstructured grid solver for the euler and Navier-Stokes equationsBased on a paper originally presented at the AIAA 26th Aerospace Sciences Meeting, Reno, Nevada, January 1988. (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 405-425 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Euler equations ; Finite element ; Hypersonic laminar-viscous flow ; Time marching ; Shock wave interactions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An upwind finite element technique that uses cell-centred quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive triangular grids. The approach is an extension to unstructured grids of the LAURA algorithm due to Gnoffo. A structured grid of quadrilaterals is laid out near a solid surface. For inviscid flows the method is stable at Courant numbers of over 100000. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view to simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are distinctly captured with a sequence of adaptively generated grids.
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    A finite element method for analysis of fluid flow, heat transfer and free interfaces in Czochralski crystal growth (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 453-492 
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    ISSN: 0271-2091
    Keywords: Czochralski crystal growth ; Finite element method ; Free boundary problem ; Incompressible fluid flow ; Heat transfer ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element algorithm is presented for simultaneous calculation of the steady state, axisymmetric flows and the crystal, melt/crystal and melt/ambient interface shapes in the Czochralski technique for crystal growth from the melt. The analysis is based on mixed Lagrangian finite element approximations to the velocity, temperature and pressure fields and isoparametric approximations to the interface shape. Galerkin's method is used to reduce the problem to a non-linear algebraic set, which is solved by Newton's method. Sample solutions are reported for the thermophysical properties appropriate for silicon, a low-Prandtl-number semiconductor, and for GGG, a high-Prandtl-number oxide material. The algorithm is capable of computing solutions for both materials at realistic values of the Grashof number, and the calculations are convergent with mesh refinement. Flow transitions and interface shapes are calculated as a function of increasing flow intensity and compared for the two material systems. The flow pattern near the melt/gas/crystal tri-junction has the asymptotic form predicted by an inertialess analysis assuming the meniscus and solidification interfaces are fixed.
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    An inverse finite element method with an application to extrusion with solidification (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 541-555 
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    ISSN: 0271-2091
    Keywords: Inverse finite elements ; Solidification ; Extrusion ; Metal casting ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The flow and solidification of planar jets are analysed by means of an efficient inverse isotherm finite element method. The method is based on a tessellation that is constructed by isotherms as characteristic co-ordinate lines transverse to the flow direction. Thus opposite sides of finite elements lie on isotherms. The method allows the simultaneous determination of the location of the isotherms with the primary unknowns, namely, the velocity, the pressure, the temperature and the location of the free surface. Thus the determination of the location of the solidification front (which is known to pose significant computational difficulties) is automatic. This facilitates the control of the location of the solidification front by controlling macroscopic variables such as the flow rate, the cooling rate and the capillary design. The location of the solidification may then be suitably chosen to influence the frozen-in orientation and structure in extrusion of high-performance materials such as composites and polymers, in continuous casting of metals and in growth of crystals.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650090505
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    Mathematical derivation of a finite volume formulation for laminar flow in complex geometries (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 531-540 
    Details
    ISSN: 0271-2091
    Keywords: General non-orthogonal ; Complex geometries ; Viscous ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper treats the mathematical derivation of a novel formulation of the Navier-Stokes equation for general non-orthogonal curvilinear co-ordinates. The covariant velocity components are solved in this FVM formulation, which leads to the pressure-velocity coupling becoming relatively easy to handle at the expense of a more complicated expression of the convective and diffusive fluxes. When a velocity component is solved at a point P, the neighbouring velocities are projected in the direction of the velocity component at the point P. Thus the base vectors are changed at the neighbouring points. This renders a simpler expression for the covariant derivatives. Neither the Cristoffel symbol nor its derivatives need be computed. This contributes to the accuracy of the formulation. The procedure of changing the base vectors affects only the convected velocity. The convecting term (dot product of velocity and area) is calculated without any change of the base vectors. The same is true for the operator on the covariant velocity in the diffusion term.It is shown that when using upwind differencing the use of projected velocities gives better results than when curvature effects are included in the source term. The discretized equations are written in a form which enables the use of the tridiagonal matrix algorithm (TDMA). The equations can be solved using either the SIMPLEC or the PISO procedure.Two examples of laminar flows are given.
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    URL: http://dx.doi.org/10.1002/fld.1650090504
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    A calculation procedure for steady two-dimensional elliptic flows (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 609-617 
    Details
    ISSN: 0271-2091
    Keywords: Calculation procedure ; Density correction ; Elliptic flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A calculation procedure is presented for predicting steady two-dimensional elliptic flows. The method introduces a density correction concept and an algebraic equation for the velocity correction instead of the troublesome pressure correction equation in the SIMPLER procedure. Computations show that the method has the same rate of convergence as SIMPLER while saving about 20% computational effort per iteration. Although the method is described for steady two-dimensional situations, its extension to three-dimensional problems is very straightforward.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650090510
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    Low Reynolds number hydrodynamic interaction of a solid particle with a planar wall (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 651-688 
    Details
    ISSN: 0271-2091
    Keywords: Stokes flow ; Creeping flow ; Wall Green function ; Boundary integral method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The slow viscous flow problem of an arbitrary solid particle in motion near a planar wall is recast into a boundary integral formulation. The present formulation employs the Green function appropriate to the planar wall problem and is developed in sufficient generality to allow calculations for arbitrary particles in any base flow which satisfies Stokes equations and no-slip on the wall. The resulting integral equations are easily discretized and solved for the particle surface tractions. Calculations are performed for axisymmetric motions of a variety of ellipso˛ids near the planar wall. Agreement with existing theory is excellent.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650090603
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    Masthead (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090701
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    Internal wave reflections and transmissions arising from a non-uniform mesh. Part I: An analysis for the Crank-Nicolson linear finite element scheme (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 783-810 
    Details
    ISSN: 0271-2091
    Keywords: Non-uniform mesh ; Wave Reflection/transmission ; Crank-Nicolson finite elements ; Fourier analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This is the first of a series of three related papers dealing with some of the consequences of non-uniform meshes in a numerical model. In this paper the accuracy of the Crank-Nicolson linear finite element scheme, which is applied to the linear shallow water equations, is examined in the context of a single abrupt change in nodal spacing. The (in)accuracy is quantified in terms of reflection and transmission coefficients. An incident wave impinging on the interface between two regions with different nodal spacings is shown to give rise to no reflected waves and two transmitted waves. The analysis is verified using three different wavelengths (2Δx, 4Δx 8Δx) in three ‘hot-start’ numerical experiments with a mesh expansion factor of 2 and three experiments with a mesh contraction factor of 1/2. An energy flux analysis based on the concept of group velocity shows that energy is conserved across the interface.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650090704
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    Masthead (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090801
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    Some uses of Green's theorem in solving the Navier-Stokes equations (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 871-890 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Integral conditions ; Vorticity ; Pressure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper gives a review of methods where Green's theorem may be employed in solving numerically the Navier-Stokes equations for incompressible fluid motion. They are based on the concept of using the theorem to transform local boundary conditions given on the boundary of a closed region in the solution domain into global, or integral, conditions taken over it. Two formulations of the Navier-Stokes equations are considered: that in terms of the streamfunction and vorticity for two-dimensional motion and that in terms of the primitive variables of the velocity components and the pressure. In the first formulation overspecification of conditions for the streamfunction is utilized to obtain conditions of integral type for the vorticity and in the second formulation integral conditions for the pressure are found. Some illustrations of the principle of the method are given in one space dimension, including some derived from two-dimensional flows using the series truncation method. In particular, an illustration is given of the calculation of surface vorticity for two-dimensional flow normal to a flat plate. An account is also given of the implementation of these methods for general two-dimensional flows in both of the mentioned formulations and a numerical illustration is given.
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    URL: http://dx.doi.org/10.1002/fld.1650090802
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    Comparison of k-∊ and algebraic Reynolds stress models for swirling diffuser flow (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 987-1009 
    Details
    ISSN: 0271-2091
    Keywords: Turbulence ; Swirl ; Conical diffusers ; Multi-sweep ; Navier-Stokes equations ; Reynolds stress mode ; k-∊ model ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A brief overview of classes of turbulent swirling flow in conical diffusers is given, together with a description of appropriate numerical schemes for each class. Numerical results obtained for the class of moderate swirl in a 20° diffuser and for the class of no swirl in an 8° diffuser are compared with experimental results. The results are obtained using a multi-sweep scheme solving the full steady state time-averaged Navier-Stokes equations. Turbulence quantities are approximated using two types of algebraic Reynolds stress model and two types of k-∊ model. One of the algebraic Reynolds stress models includes extra production terms associated with the Christoffel symbols in cylindrical co-ordinates, and one of the k-∊ models includes a swirl-related modification to the ∊ equation. It is demonstrated that the standard k-∊model gives poor prediction of the mean flow, and it is necessary to at least use the modified form or one of the two algebraic Reynolds stress models.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650090807
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    Analysis of incompressible massively separated viscous flows using unsteady Navier-Stokes equations (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1025-1050 
    Details
    ISSN: 0271-2091
    Keywords: Unsteady Navier-Stokes equations ; Direct solution method ; Block Gaussian elimination ; Backstep channel ; Incompressible separated flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream-function in generalized curvilinear orthogonal co-ordinates to facilitate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the vorticity transport equation using the alternating direction implicit method, whereas the streamfunction equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a backstep in a doubly infinite channel, using clustered conformal co-ordinates. One-dimensional stretching functions, dependent on the Reynolds number and the asymptotic behaviour of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honour the multiple length scales of the separated flow model problem. The asymptotic behaviour of the finite differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second-order-accurate wiggle-free solutions, i.e. with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem, prior to the onset of three-dimensionality in the experiment.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650090809
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    Assessment of variants of the k-∊ turbulence model for engine flow applications (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1073-1086 
    Details
    ISSN: 0271-2091
    Keywords: k-∊ turbulence model ; Compressible flow ; Bulk dilatation ; Reciprocating engine flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with simulation of the mean flow and turbulence evolution in a model engine and comparison of the behaviour of certain important turbulence parameters, namely the intensity, length scale and dissipation time scale, as predicted by three variants of the k-∊ model developed for application to strongly compressible flows. The predictions pertain to the axisymmetric, disc-chamber, four-stroke, Imperial College model engine operating at 200 rpm and compression ratios of 3·5 and 6·7. The paper analyses the predicted variations of these parameters during the induction, compression and expansion strokes and identifies the versions that produce the most consistent and physically plausible variations. The significance, to the turbulence evolution, of the ratio of the turbulence dissipation time scale to the time scale of compression/expansion is also discussed. It is concluded that on these grounds the Morel-Mansour and El Tahry versions are, and the Watkins version is not, suitable for engine applications.
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    URL: http://dx.doi.org/10.1002/fld.1650090903
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    A fast riemann solver with constant covolume applied to the random choice method (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1145-1164 
    Details
    ISSN: 0271-2091
    Keywords: Riemann problem ; Covolume ; Random choice ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Riemann problem for the unsteady one-dimensional Euler equations together with the constant-covolume equation of state is solved exactly. The solution is then applied to the random choice method to solve the general initial-boundary value problem for the Euler equations. The iterative procedure to find p*, the pressure between the acoustic waves, involves a single algebraic (non-linear) equation, all other quantities follow directly throughout the x-t plane, except within rarefaction fans where an extra iterative procedure is required. The solution is validated against existing exact results both directly and in conjunction with the random choice method.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650090908
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    On the application of pseudospectral FFT techniques to non-periodic problems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1235-1267 
    Details
    ISSN: 0271-2091
    Keywords: Pseudospectral ; Non-periodic ; Incompressible flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The reduction-to-periodicity method using the pseudospectral fast Fourier transform (FFT) technique is applied to the solution of non-periodic problems, including the two-dimensional incompressible Navier-Stokes equations. The accuracy of the method is explored by calculating the derivatives of given functions, one- and two-dimensional convective-diffusive problems, and by comparing the relative errors due to the FFT method with a second-order finite difference (FD) method. Finally, the two-dimensional Navier-Stokes equations are solved by a fractional step procedure using both the FFT and the FD methods for the driven cavity flow and the backward-facing step problems. Comparisons of these solutions provide a realistic assessment of the FFT method.
    Additional Material: 26 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650091006
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    Masthead (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091101
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    A comparison of primitive variables and streamfunction-vorticity for fem depth-averaged modelling of steady flow (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1369-1379 
    Details
    ISSN: 0271-2091
    Keywords: Depth-averaged flow ; Finite elements ; Streamfunction-vorticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The governing equations for depth-averaged turbulent flow are presented in both the primitive variable and streamfunction-vorticity forms. Finite element formulations are presented, with special emphasis on the handling of bottom stress terms and spatially varying eddy viscosity. The primitive variable formulation is found to be preferable because of its flexibility in handling spatial variation in viscosity, variability in water surface elevations, and inflow and outflow boundaries. The substantial reduction in computational effort afforded by the streamfunction-vorticity formulation is found not to be sufficient to recommend its use for general depth-averaged flows. For those flows in which the surface can be approximated as a fixed level surface, the streamfunction-vorticity form can produce results equivalent to the primitive variable form as long as turbulent viscosity can be estimated as a constant.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650091106
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    Convergence properties of high-Reynolds-number separated flow calculations (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1395-1411 
    Details
    ISSN: 0271-2091
    Keywords: Reduced Navier-Stokes computations ; Flow separation ; Laminar instability ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The convergence properties of an iterative solution technique for the Reduced Navier-Stokes equations are examined for two-dimensional steady subsonic flow over bump and trough geometries. Techniques for decreasing the sensitivity to the initial pressure approximation, for fine meshes in particular, are investigated. They are shown to improve the robustness of the relaxation process and to decrease the computational work required to obtain a converged solution. A semi-coarsening multigrid technique that has previously been found to be particularly advantageous for high-Reynolds-number (Re) flows with flow separation and with highly stretched surface-normal grids is applied herein to further accelerate convergence. Solutions are obtained for the laminar flow over a trough that is more severe than has been considered to date. Sufficient axial grid refinement in this case leads to a shock-like reattachment and, for sufficiently large Re, to a local ‘divergence’ of the numerical computations. This ‘laminar flow breakdown’ appears to be related to an instability associated with high-frequency fine-grid modes that are not resolvable with the present modelling. This behaviour may be indicative of dynamic stall or of incipient transition. The breakdown or instability is shown to be controllable by suitable introduction of transition turbulence models or by laminar flow control, i.e. small amounts of wall suction. This lends further support to the hypothesis that the instability is of a physical rather than numerical character and suggests that full three-dimensional analysis is required to properly capture the flow behaviour. Another inference drawn from this investigation is that there is a need for careful grid refinement studies in high-Re flow computations, since coarser grids may yield oscillation-free solutions that cannot be obtained on finer grids.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650091108
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    Masthead (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091201
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    Probabilistic approach for transport of contaminants through porous mediaPaper presented at the ASME Winter Annual Meeting, December 1987. (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1431-1451 
    Details
    ISSN: 0271-2091
    Keywords: Probabilistic diffusion-convection equation ; Gaussian field approach ; Random walk method ; Fluctuation Peclet number ; Porous media ; Two-phase system ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The channels formed between individual particles in porous media have variable dimensions and orientations. The porosity, permeability and its anisotropy exhibit random spatial distributions. The probabilistic approach can effectively describe the transport of contaminants through porous media and is analysed in this paper. Numerical results are obtained by considering (I) random dispersion coefficients without and with spatial structure, (II) random time distribution of concentration at the inlet boundary, (III) random velocity distribution in the flow field without and (IV) with variable dispersion coefficient, (V) non-linearity of the governing equation and (VI) anisotropy of the dispersion coefficient. Two methods are used for probabilistic predictions: (1) Gaussian field approach in conjunction with Monte Carlo method and (2) random walk method. The input random parameters are assumed to have normal and log-normal distributions according to available experimental data. The probability distribution functions of the contaminant concentration at different locations within the flow domain are calculated and compared with the input distributions as a function of the mean and fluctuation Peclet numbers. The one-dimensional case is analysed in detail and the illustrative numerical predictions are compared with analytical and experimental results. The extension to a two-dimensional domain is discussed in the last part of this paper.
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    URL: http://dx.doi.org/10.1002/fld.1650091202
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    Marangoni convection in weld pools with a free surface (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1503-1516 
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    ISSN: 0271-2091
    Keywords: Welding ; Free surface ; Marangoni convection ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A steady-state two-dimensional model of heat transfer and fluid flow was developed to describe Marangoni convection in the weld pool. Both the pool surface and the fusion boundary were calculated. The validity of the model was verified against an asymptotic solution for Marangoni-convection-induced free surface geometry. Two different cases were studied, i.e. a negative surface tension temperature coefficient ∂γ/∂T a positive one, and the resultant shapes of the weld pool surface were compared.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650091206
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    A multigrid method for steady incompressible Navier-Stokes equations based on partial flux splitting (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 113-120 
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    ISSN: 0271-2091
    Keywords: Steady Navier-Stokes equations ; Partial flux splitting ; Multigrid methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Flux splitting is applied to the convective part of the steady Navier-Stokes equations for incompressible flow. Partial upwind differences are introduced in the split first-order part, while central differences are used in the second-order part. The discrete set of equations obtained is positive, so that it can be solved by collective variants of relaxation methods. The partial upwinding is optimized in the same way as for a scalar convection-diffusion equation, but involving several Peclet numbers. It is shown that with the optimum partial upwinding accurate results can be obtained. A full multigrid method in W-cycle form, using red-black successive under-relaxation, injection and bilinear interpolation, is described. The efficiency of this method is demonstrated.
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    URL: http://dx.doi.org/10.1002/fld.1650090109
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    Performance of iterative methods for Newtonian and generalized Newtonian flows (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 127-150 
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    ISSN: 0271-2091
    Keywords: Iterative solution ; Viscous flow ; Generalized conjugate gradient ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We consider the use of accelerated gradient-type iterative methods for solution of Newtonian and certain non-Newtonian (power-law and Bingham models) viscous flow problems. The formulations are based on penalty and mixed finite element methods, and such factors as the effect of the penalty parameter, asymmetry, continuation and preconditioning are examined.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650090202
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    Effects of grid staggering on numerical schemes (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 193-212 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Staggered grid ; Primitive variable formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Nine finite difference schemes using primitive variables on various grid arrangements were systematically tested on a benchmark problem of two-dimensional incompressible Navier-Stokes flows. The chosen problem is similar to the classical lid-driven cavity flow, but has a known exact solution. Also, it offers the reader an opportunity to thoroughly evaluate accuracies of various conceptual grid arrangements.Compared to the exact solution, the non-staggered grid scheme with higher-order accuracy was found to yield an accuracy significantly better than others. In terms of ‘overall performance’, the so-called 4/1 staggered grid scheme proved to be the best. The simplicity of this scheme is the primary benefit. Furthermore, the scheme can be changed into a non-staggered grid if the pressure is replaced by the pressure gradient as a field variable.Finally, the conventional staggered grid scheme developed by Harlow and Welch also yields relatively high accuracy and demonstrates satisfactory overall performance.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090206
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  • 94
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    Electronic Resource
    Masthead (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090301
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  • 95
    Electronic Resource
    Electronic Resource
    A finite element analysis of the steady laminar entrance flow in a 90° curved tube (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 275-287 
    Details
    ISSN: 0271-2091
    Keywords: Curved pipe flow ; Entrance flow ; Finite element method ; Penalty function method ; Experimental validation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A standard Galerkin finite element penalty function method is used to approximate the solution of the three-dimensional Navier-Stokes equations for steady incompressible Newtonian entrance flow in a 90° curved tube (curvature ratio δ = 1/6) for a triple of Dean numbers (κ = 41, 122 and 204). The computational results for the intermediate Dean number (κ = 122) are compared with the results of laser-Doppler velocity measurements in an equivalent experimental model. For both the axial and secondary velocity components, fair agreement between the computational and experimental results is found.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090304
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  • 96
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    Electronic Resource
    Three-dimensional unsteady flow simulations: Alternative strategies for a volume-averaged calculation (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 341-362 
    Details
    ISSN: 0271-2091
    Keywords: Unsteady ; Fluid flow ; Navier-Stokes ; Simulation ; SIMPLE ; PRIME ; QUICK ; ICCG ; MG ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This work builds on a SIMPLE-type code to produce two numerical codes of greatly improved speed and accuracy for solution of the Navier-Stokes equations. Both implicit and explicit codes employ an improved QUICK (quadratic upstream interpolation for convective kinematics) scheme to finite difference convective terms for non-uniform grids. The PRIME (update pressure implicit, momentum explicit) algorithm is used as the computational procedure for the implicit code. Use of both the ICCG (incomplete Cholesky decomposition, conjugate gradient) method and the MG (multigrid) technique to enhance solution execution speed is illustrated. While the implicit code is first-order in time, the explicit is second-order accurate. Two- and three-dimensional forced convection and sidewall-heated natural convection flows in a cavity are chosen as test cases. Predictions with the new schemes show substantial computational savings and very good agreement when compared to previous simulations and experimental data.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090308
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  • 97
    Electronic Resource
    Electronic Resource
    Numerical simulation of the hydrodynamic interaction between a sedimenting particle and a neutrally buoyant particle (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 263-273 
    Details
    ISSN: 0271-2091
    Keywords: Low-Reynolds-number flow ; Sedimentation ; Hydrodynamic interactions ; Two-phase flows ; Suspensions ; Boundary element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new method for the simulation of the translational and rotational motions of a system containing a sedimenting particle interacting with a neutrally buoyant particle has been developed. The method is based on coupling the quasi-static Stokes equations for the fluid with the rigid body equations of motion for the particles. The Stokes equations are solved at each time step with the boundary element method. The stresses are then integrated over the surface of each particle to determine the resultant forces and moments. These forces and moments are inserted into the rigid body equations of motion to determine the translational and rotational motions of the particles. Unlike many other simulation techniques, no restrictions are placed on the shape of the particles. Superparametric boundary elements are employed to achieve accurate geometric representations of the particles. The simulation method is able to predict the local fluid velocity, resolve the forces and moments exerted on the particles, and track the particle trajectories and orientations.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090303
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  • 98
    Electronic Resource
    Electronic Resource
    Announcement (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 498-498 
    Details
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090408
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  • 99
    Electronic Resource
    Electronic Resource
    A finite element analysis of a free surface drainage problem of two immiscible fluids (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 569-582 
    Details
    ISSN: 0271-2091
    Keywords: Flow analysis ; Free surface problem ; Finite element method ; Blast furnace ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A sharp interface problem arising in the flow of two immiscible fluids, slag and molten metal in a blast furnace, is formulated using a two-dimensional model and solved numerically. This problem is a transient two-phase free or moving boundary problem, the slag surface and the slag-metal interface being the free boundaries. At each time step the hydraulic potential of each fluid satisfies the Laplace equation which is solved by the finite element method. The ordinary differential equations determining the motion of the free boundaries are treated using an implicit time-stepping scheme. The systems of linear equations obtained by discretization of the Laplace equations and the equations of motion of the free boundaries are incorporated into a large system of linear equations. At each time step the hydraulic potential in the interior domain and its derivatives on the free boundaries are obtained simultaneously by solving this linear system of equations. In addition, this solution directly gives the shape of the free boundaries at the next time step. The implicit scheme mentioned above enables us to get the solution without handling normal derivatives, which results in a good numerical solution of the present problem. A numerical example that simulates the flow in a blast furnace is given.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090507
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  • 100
    Electronic Resource
    Electronic Resource
    Upwind basis finite elements for convection-dominated problems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 385-403 
    Details
    ISSN: 0271-2091
    Keywords: Upwind ; QUICK ; Petrov-Galerkin ; Convection-diffusion ; Advection ; Navier-Stokes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Finite elements using higher-order basis functions in the spirit of the QUICK method for convection-dominated fluid flow and transport problems are introduced and demonstrated. Instead of introducing new internal degrees of freedom, completeness is achieved by including functions based on nodal values exterior and upwind to the element domain. Applied with linear test functions to the weak statements for convection-dominated problems, a family of Petrov-Galerkin finite elements is developed. Quadratic and cubic versions are demonstrated for the one-dimensional convection-diffusion test problem. Elements of up to seventh degree are used for local solution refinement. The behaviour of these elements for one-dimensional linear and non-linear advection is investigated. A two-dimensional quadratic upwind element is demonstrated in a streamfunction-vorticity formulation of the Navier-Stokes equations for a driven cavity flow test problem. With some minor reservations, these elements are recommended for further study and application.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090403
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