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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988) 
    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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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 659-669 
    ISSN: 0271-2091
    Keywords: Magnetohydrodynamics ; Homotopy ; Quasi-Newton ; Rotating disk ; 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 studies the effects of a circular magnetic field on the flow of a conducting fluid about a porous rotating disk. Using modern quasi-Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magnetic field strengths, suction and injection velocities and Alfven and disk speeds. Results are presented graphically in terms of three non-dimensional parameters. There is excellent agreement with previous work and asymptotic formulae.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 671-686 
    ISSN: 0271-2091
    Keywords: Multigrid ; Pressure correction ; 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: The behaviour of the pressure correction method is studied for the solution of the incompressible steady-state Navier-Stokes and continuity equations in a rotating cylindrical-polar co-ordinate system, the specific problem being that of laminar source-sink flow between two corotating discs. Modifications to improve the linearization and the handling of the rotation terms are introduced, and we compare three extended pressure correction schemes and also the use of a multigrid algorithm in part of the calculation procedure as a linear solver.
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  • 4
    ISSN: 0271-2091
    Keywords: Finite Element ; Quasi-three-dimensional ; Interconnected Aquifer Systmes ; Fluid Mass Balance ; Iterated Frontal Method ; Predictor-Corrector 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 quasi-three-dimensional equations controlling the groundwater flow in heterogeneous and interconnected aquifer systems are discretized by finite elements, considering also the aquifer branching. A new method for fluid mass balance evaluation based on the equivalent nodal source (E.N.S.) concept allows one to express the balance in conservative terms, and interpret finite element equations as nodal balance equations. The solution of the system is based on the frontal method. Use of substructures limits the frontal increase in correspondence to the aquifer branching. In the steady state, the frontal method is integrated with an iterative solution technique to eliminate the frontal increase caused by the presence of aquitards. It converges very rapidly, using a forcing technique with an automatic parameter definition. In the unsteady case the same scope is achieved using a predictor-corrector procedure which employs the Crank-Nicolson method in the corrector phase.This very stable procedure permits use of fairly long time-steps and concerns the case of source terms depending on piezometry (problem of interaction between water table and river). This method has been tested with several fairly complex cases.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 493-506 
    ISSN: 0271-2091
    Keywords: Modified ; Dodge ; Algorithm ; Parabolized ; Navier-Stokes ; Computational Fluid Dynamics ; Low Speed Flow ; Channel Flow ; Zebra Algorithm ; Mass Balancing ; 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 revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow has been developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (chequerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A chequerboard iteration is ued to solve the resulting implicit non-linear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results has been obtained for some flows with well-known solutions.
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  • 6
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 965-975 
    ISSN: 0271-2091
    Keywords: Finite element method ; Turbulent flow ; Method of characteristics ; Penalty function approach ; Galerkin 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 technique is presented and applied to some one- and two-dimensional turbulent flow problems. The basic equations are the Reynolds averaged momentum equations in conjunction with a two-equation (k, ∊) turbulence model. The equations are written in time-dependent form and stationary problems are solved by a time iteration procedure. The advection parts of the equations are treated by the use of a method of characteristics, while the continuity requirement is satisfied by a penalty function approach. The general numerical formulation is based on Galerkin's method. Computational results are presented for one-dimensional steady-state and oscillatory channel flow problems and for steady-state flow over a two-dimensional backward-facing step.
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  • 7
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 989-990 
    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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  • 8
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 991-994 
    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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  • 9
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 1029-1036 
    ISSN: 0271-2091
    Keywords: Incompressible Flow ; Pressure Poisson Equation ; Inviscid Flow ; 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: In a recent paper Gresho and Sani showed that Dirichlet and Neumann boundary conditions for the pressure Poisson equation give the same solution. The purpose of this paper is to confirm this (for one case at least) by numerically solving the pressure equation with Dirichlet and Neumann boundary conditions for the inviscid stagnation point flow problem. The Dirichlet boundary condition is obtained by integrating the tangential component of the momentum equation along the boundary. The Neumann boundary condition is obtained by applying the normal component of the momentum equation at the boundary. In this work solutions for the Neumann problem exist only if a compatibility condition is satisfied. A consistent finite difference procedure which satisfies this condition on non-staggered grids is used for the solution of the pressure equation with Neumann conditions. Two test cases are computed. In the first case the velocity field is given from the analytical solution and the pressure is recovered from the solution of the associated Poisson equation. The computed results are identical for both Dirichlet and Neumann boundary conditions. However, the Dirichlet problem converges faster than the Neumann case. In the second test case the velocity field is computed from the momentum equations, which are solved iteratively with the pressure Poisson equation. In this case the Neumann problem converges faster than the Dirichlet problem.
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  • 10
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 529-542 
    ISSN: 0271-2091
    Keywords: Strongly Rotating ; Incompressible ; Free-surface ; Finite-difference ; Coriolis ; 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 of an incompressible fluid in a rapidly rotating right circular cylinder is considered. A source/sink mass distribution at the lateral wall, which is azimuthally uniform and symmetric across the midplane, causes a deviation from wheel flow. The container is only partially full and the inner free surface is allowed to deviate slightly from the vertical. A finite-difference solution of the full axisymmetric, non-linear governing equations was used to obtain the flow field. A special implicit technique for the Coriolis terms which maintains geostrophy was developed and is described. The results obtained for a low Rossby number flow compare quite favourably with the linearized solution. Results are also presented for a case wherein the non-linear terms are important.
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  • 11
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 567-581 
    ISSN: 0271-2091
    Keywords: Advection ; Convection ; Estuary ; Fractional ; Step ; Diffusion ; Dispersion ; Moving ; Co-ordinates 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: A successful and economical fractional step algorithm for the convection-dispersion-reaction equation is described. Exact solutions are adopted for the reaction and convection steps, the latter by the introduction of a moving co-ordinate system. The dispersion step uses an optimized finite difference algorithm which specifically accommodates the grid non-uniformity. The excellent performance of the algorithm is confirmed by numerical experiments together with computations of the Fourier response and integrated square error characteristics.
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  • 12
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 583-590 
    ISSN: 0271-2091
    Keywords: QUICK ; Finite Difference ; 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: The spatially third-order accurate QUICK finite difference technique is applied to the solution of the depth-integrated equations of motion for steady, subcritical, free surface flow in a wide, shallow, rectangular channel with and without an abrupt expansion. The conservative, control-volume discretization of the equations of motion and the use of QUICK in approximating required cell and cell face average quantities is discussed. Results presented show that it is possible to obtain stable solutions for advective free surface flows without resorting to implicit numerical smoothing.
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  • 13
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984) 
    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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  • 14
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 591-604 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; Finite Element Method ; Wave Equation ; Numerical Noise ; 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 noise has been a problem with finite element solutions to the shallow water equations. Two methods used to reduce the noise level are evaluated, and these results are compared with published results for equal-order interpolations. The two methods are mixed-interpolation (quadratic interpolation for velocity and linear interpolation for sea level) and a spectral form of the wave equation. Whereas mixed interpolation removes the troublesome sea level mode, it can still have considerable noise in velocity. The spectral wave equation is efficient and does not contain the spurious eigenmodes which contribute to high noise levels.
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  • 15
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 1-12 
    ISSN: 0271-2091
    Keywords: Review ; Finite Elements ; Meteorology ; 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 application of the finite-element method to the simulation of meterological fluid flow problems is reviewed. Early studies were aimed primarily at demonstrating the viability of the method for one- and two-dimensional flows, whereas more recent studies have been aimed at demonstrating the efficiency and viability of the method for more complex three-dimensional simulations. There has also been a shift towards exploiting such models to better understand and predict the underlying meteorological phenomena, rather than restricting attention to the development of the algorithms.
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  • 16
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 605-622 
    ISSN: 0271-2091
    Keywords: Natural ; Convection ; Stream ; Function ; Finite ; Element ; Formulation ; C1 ; Continuity ; Truncated ; Quintic ; Restricted Variational Principle ; 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 stream function formulation is presented for the solution to the two-dimensional double-glazing problem. Laminar flow with constant properties is considered and the Boussinesq approximation used. A restricted variational principle is used, in conjunction with a triangular finite element of C1 continuity, to discretize the two coupled governing partial differential equations (4th order in stream function and second order in temperature). The resulting non-linear system of equations is solved in a segregated (decoupled) manner by the Newton-Raphson linearizing technique.Results are produced for the standard test case of an upright square cavity. These are for Rayleigh numbers in the range 103-105, with a Prandtl number of 0.71. Comparisons are made with benchmark results presented at the 1981 International Comparison study in Venice. In the discussion of results, emphasis is placed on the variation of local Nusselt number along the isothermal walls, particularly near the corner. This reveals a noticeable source of error in the evaluation of the maximum Nusselt number by lower order discretization methods.
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  • 17
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 1117-1118 
    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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  • 18
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1107-1116 
    ISSN: 0271-2091
    Keywords: Numerical Stability ; Eddy Viscosity ; LES ; 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 spectral LES code it is not possible to treat the actual eddy viscosity implicitly. We have therefore examined the effect on stability of adding a constant pseudo-viscosity to the implicit term and subtracting it from the explicit term: stability limits have been derived theoretically and verified computationally for two different treatments of the explicit term. We have also studied the effect of a stochastic temporal variation of the eddy viscosity.
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  • 19
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1135-1149 
    ISSN: 0271-2091
    Keywords: Three-dimensional unstructured grids ; Advancing-front technique ; Grid generation ; 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 generation of three-dimensional unstructured grids using the advancing-front technique is described. This technique has been shown to be effective for the generation of unstructured grids in two dimensions.1,2 However, its extension to three-dimensional regions required algorithms to define the surface and suitable data structures that avoid excessive CPU-time overheads for the search operations involved. After obtaining an initial triangulation of the surfaces, tetrahedra are generated by successively deleting faces from the generation front. Details of the grid generation algorithm are given, together with examples and timings.
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  • 20
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1183-1193 
    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
    Notes: The different stages of bursting and evolution of the fluctuation field in a turbulent boundary layer are governed by mechanisms that may be identified as either predominantly linear, i.e. governed by linear interaction with the mean shear flow, or non-linear, i.e. with interaction between the fluctuation components also being important. Wave number-frequency spectra reveal the presence of damped wave modes that may be modelled from the Orr-Sommerfeld equation. Conditional sampled experimental data for streamwise velocity fluctuations in the wall layer obtained using the variable interval time averaging (VITA) method scale with the threshold level in a manner consistent with linearity. High-amplitude wall pressure peaks show an approximately linear relationship with the associated vertical velocity fluctuations. Non-linearity acts primarily in the near-wall region where the fluctuation velocity is relatively the highest.
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  • 21
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 105-105 
    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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  • 22
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1367-1388 
    ISSN: 0271-2091
    Keywords: Laminar boundary layer ; Splines Incompressible ; Inverse and direct 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: A unified approach is presented for solving the two-dimensional incompressible boundary layer equations. Solutions are obtained for direct and inverse options using the same equation formulation by a simple interchange of boundary conditions. A modified form of the mechul function scheme obtains inverse solutions with specification of transformed wall shear, skin friction coefficient or displacement thickness distributions. Direct solutions may be obtained without altering the block tridiagonal structure of the system by simply requiring no corrections on the streamwise pressure gradient parameter. Fourth-order spline discretization approximates normal derivatives with two- and three-point backward differences approximating streamwise derivatives, yielding a fully implicit solution method. The resulting spline/finite difference equations are solved by Newton-Raphson iteration together with partial pivoting. The results of the study demonstrate the importance of proper linearization of all equations. The successful use of spline discretization is also tied to the use of strong two-point boundary conditions at the wall for cases involving reversed flow. Numerical solutions are presented for several non-similar flows and compared with published results.
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  • 23
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1389-1401 
    ISSN: 0271-2091
    Keywords: Non-Newtonian fluid interfaces ; Porous media ; Frontal advance theory ; Power law behaviour ; Oil displacement mechanisms ; 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 concerns the applications of frontal advance theory to the dynamics of a moving flat interface in a porous medium, when both displacing and displaced fluids are of power law behaviour. The rheological effects of non-Newtonian behaviour of these fluids on the interface position and its velocity are numerically illustrated and discussed with regard to the practical implications in oil displacement mechanisms. The results obtained should be useful in finding an optimal policy of injection in order to control the dynamics of the moving interface in field projects of enhanced oil recovery floods.
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  • 24
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1465-1466 
    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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  • 25
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    International Journal for Numerical Methods in Fluids 8 (1988) 
    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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  • 26
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1587-1588 
    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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  • 27
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1563-1586 
    ISSN: 0271-2091
    Keywords: Finite element ; Turbulence model ; Free shear 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: This paper reviews past and current efforts in developing a simple but robust turbulence model for free shear flows. Much of this work has been published previously and this paper is a rearrangement aimed at the conference. The model is presented and is interfaced with FIDAP to solve three-dimensional flows and a pusher - prop configuration. The eight-node brick, the penalty formulation and the Broyden method are used to solve the Navier-Stokes equations. The propeller is modelled as an actuator disc and the direct simulation of a given propeller is considered in detail. Good results are obtained for the square jet. For propeller cases detailed comparison with wind tunnel measurements shows excellent prediction of the velocity and pressure for flows of this complexity.
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  • 28
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 147-158 
    ISSN: 0271-2091
    Keywords: Finite Element ; Incompressible Flow ; Pressure-specification-point ; 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 discontinuity of a finite-element pressure field that is sometimes present in the neighbourhood of the pressure-specification-point is shown to arise either from round-off, or from mistakes in modelling. The implications of this are considered. In particular it restricts grid refinement near the pressure-specification-point. The analysis can be extended to finite-difference calculations, and to other fields governed by equations similar to Poisson's equation.
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  • 29
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 275-287 
    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.
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  • 30
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 109-125 
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-Stokes ; Vorticity-stream function ; Time-dependent ; flows ; Boundary conditions ; Incompressible viscous flows ; Two-dimensional 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 new finite element method for solving the time-dependent incompressible Navier-Stokes equations with general boundary conditions is presented. The two second-order partial differential equations for the vorticity and the stream function are factorized, apart from the non-linear advection term, by eliminating the coupling due to the double specification on the stream function at (a part of) the boundary. This is achieved by reducing the no-slip boundary conditions to projection integral conditions for the vorticity field and by evaluating the relevant quantities involved according to an extension of the method of Glowinski and Pironneau for the biharmonic problem. Time integration schemes and iterative algorithms are introduced which require the solution only of banded linear systems of symmetric type. The proposed finite element formulation is compared with its finite difference equivalent by means of a few numerical examples. The results obtained using 4-noded bilinear elements provide an illustration of the superiority of the finite element based spatial discretization.
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  • 31
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1523-1541 
    ISSN: 0271-2091
    Keywords: Heat exchanger ; Three-dimensional flow ; Finite elements ; FIDAP ; 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 code FIDAP was used to examine the fluid flow path within a flat plate tube/fin heat exchanger and the resulting heat transfer from the fins and tube walls. The mathematical formulation, mesh development and analysis procedure are presented, and the results obtained are compared with experimental observations of the fluid flow and measurements of the fluid heating. This problem illustrates the capabilities of finite element techniques for analysing complex three-dimensional convection-dominated heat transfer, and demonstrates the scope of problems which can be addressed on a Micro VAX II/GPX workstation.
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  • 32
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    International Journal for Numerical Methods in Fluids 8 (1988), S. 1588-1588 
    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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  • 33
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    International Journal for Numerical Methods in Fluids 9 (1989) 
    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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  • 34
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 127-150 
    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.
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  • 35
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    International Journal for Numerical Methods in Fluids 4 (1984) 
    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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  • 36
    ISSN: 0271-2091
    Keywords: Polymer Flows ; Non-Newtonian ; Moving Boundary ; 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: Recent progress in the simulation of polymeric flows of two key problems in the injection moulding process, carried out by a team at Cornell University, is briefly described. For the filling of cooled thin cavities, the fluid is characterized by a power-law viscosity with exponential temperature dependence, and interaction between the transient thermal boundary-layer and the core flow in a domain with moving boundary is essential. The earlier procedure of Hieber and Shen is modified in two aspects: a boundary-integral formulation replaces the finite-element treatment of the pressure, and an ‘energy integral’ approach is used for the transient temperature. The second problem is the steady visco-elastic flow in the juncture region where sudden changes of the geometry and large strain rates occur. The constitutive equation is postulated according to the Leonov model. The main features in the numerical implementation are: integration along a streamline to determine the elastic deformation tensors for a given velocity field, and finite-element treatment (in time-dependent form) of the pressure and fields for given stresses. In an example where the contraction ratio is 7:1, results for nominal Deborah number exceeding 100 show no numerical instability. (However, for this problem, the true Weissenberg number, i.e. the ratio of local first-normal-stress difference to shear stress turns out to be generally O(10).) The predictions also correlate very well with experimental birefringence measurements.
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  • 37
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 151-165 
    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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  • 38
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 185-191 
    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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  • 39
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 193-212 
    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.
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  • 40
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 251-262 
    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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  • 41
    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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  • 42
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 303-319 
    ISSN: 0271-2091
    Keywords: Finite Element ; Turbulent 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: Although the finite-element (FE) method has been successful in analysing complex laminar flows, a number of difficulties can arise when two-equation turbulence models (e.g. the k-∊ model) are incorporated. This work describes a particular FE discretization of the k-∊ model and reports its performance in recirculating flow. Severe problems encountered in attempts to obtain convergence of the numerical scheme are isolated and analysed, and methods by which the problems can be overcome are suggested.Insight gained in this work has enabled a practical turbulent flow FE code to be constructed which is robust and efficient. This code is the subject of a further paper.
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  • 43
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 321-336 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Incorporation of the k-∊ turbulence model into Galerkin finite-element fluid-flow codes (which, unlike upwind finite-difference codes, have no artificial damping) can lead to severe iterative convergence difficulties. This paper introduces an alternative turbulence model (the q-f model) and an associated finite-element discretization method which are designed to overcome these problems. The new model forms the basis of a finite-element fluid-flow code which is robust and efficient. Furthermore, it is demonstrated on a practical example that the code can give good agreement with experiment on fairly coarse meshes.
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  • 44
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 623-650 
    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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  • 45
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 689-712 
    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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  • 46
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 747-761 
    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.
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  • 47
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 399-419 
    ISSN: 0271-2091
    Keywords: Laminar Boundary Layers ; Finite Element Method ; Finite Difference Method ; Spectral Method Convergence ; Computational Efficiency ; 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 Dorodnitsyn boundary later formulation is given a finite element interpretation and found to generate very accurate and economical solutions when combined with an implicit, non-iterative marching scheme in the downstream direction. The algorithm is of order (Δ2u, Δx) whether linear or quadratic elements are used across the boundary layer. Solutions are compared with a Dorodnitsyn spectral formulation and a conventional finite difference formulation for three Falkner-Skan pressure gradient cases and the flow over a circular cylinder. With quadratic elements the Dorodnitsyn finite element formulation is approximately five times more efficient than the conventional finite difference formulation.
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  • 48
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 421-439 
    ISSN: 0271-2091
    Keywords: Laminar Flow ; Turbulent Flow ; Compressible Flow ; Separation ; Time-split Method ; 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 time-split finite element method is extended to compute laminar and turbulent flows with and without separation. The examples considered are the flows past trailing edges of a flat plate and a backward-facing step. Eddy viscosity models are used to represent effects of turbulence. It is found that the time-split method produces results in agreement with previous experimental and computational results. The eddy viscosity models employed are found to give accurate predictions in all regions of flow except downstream of reattachment.
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  • 49
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 441-457 
    ISSN: 0271-2091
    Keywords: Finite Element Method ; Dip Coating ; Newtonian Fluid ; Free Surface ; 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 simulation of the dip coating process based on a discretization of the continuum with discontinuous pressure elements is presented. The algorithm computes the flow field from natural boundary conditions while an extra condition provided by the existence of free surface is employed to displace the meniscus location towards the actual position. The process is iterative and uses a pseudo-time stepping technique coupled to a cubic spline fitting of the free surface. Numerical predictions exhibit good agreement with experimental data for Newtonian fluids in the case of flat plate dip coating as well as in the case of wire dip coating.
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  • 50
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 459-475 
    ISSN: 0271-2091
    Keywords: Augmented Lagrangian ; Finite Element Method ; Dip Coating ; Non-Newtonian 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: We apply in this paper the augmented Lagrangian method to the study of various non-Newtonian fluid flow problems, and in particular the dip coating process. We only present in this second part the treatment specific to the non-linearities involved in the constitutive equations, the first part having largely been concerned with the general description of the approximation used.Two rheological models illustrating different rheological behaviours are used to simulate dip coating process: the Carreau-A model for shear-thinning properties of the viscosity and a truncated second-order model for a Newtonian behaviour in viscosity with elastic properties.Numerical predictions show a very good agreement with experimental data for the second-order model. The discrepancy observed in the other case can be explained qualitatively by the elastic properties exhibited by the shear-thinning fluids used: this elasticity is not taken into account in the Carreau-A model.
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  • 51
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 921-941 
    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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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1011-1024 
    ISSN: 0271-2091
    Keywords: Inviscid flow ; TVD difference scheme ; Shock wave ; Expansion wave ; 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 improved treatment for the Harten-Yee and Chakravarthy-Osher TVD numerical flux functions in general co-ordinates is presented. The proposed formulation is demonstrated by a series of numerical experiments for three-dimensional flows around the ONERA-M6 wing. The numerical results indicate that it is important to use a suitable artificial compression parameter in order to obtain more accurate solutions around the leading edge of the wing. The two TVD numerical fluxes give excellent results: they capture the shock wave without numerical oscillations, they capture the rapid expansion around the leading edge sharply, they have self-adjusting mechanisms regarding numerical viscosity and they also have robustness.
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1025-1050 
    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.
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1073-1086 
    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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  • 55
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1121-1143 
    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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  • 56
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1179-1182 
    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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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1195-1206 
    ISSN: 0271-2091
    Keywords: Free boundary problem ; Potential flow ; Wave resistance ; BEM ; 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 this paper a numerical method to compute the wave resistance of a body submerged in a free stream of finite and infinite depth is presented. Non-linear effects on the free surface are taken into account by an iterative procedure; the solution is in the form of a single-layer potential. For the 2D problem, results are shown for both the cases of finite and infinite depth of the fluid domain, with special emphasis on the supercritical flow in which the consistency of the scheme is pointed out. The method is also extended to the 3D case of a spheroid submerged in deep water. All the results presented are compared with experimental data and analytical solutions available in the literature.
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1235-1267 
    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.
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1269-1283 
    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.
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1145-1164 
    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.
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    International Journal for Numerical Methods in Fluids 9 (1989) 
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    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 62
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1207-1219 
    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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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1299-1301 
    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.
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    International Journal for Numerical Methods in Fluids 9 (1989) 
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    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 65
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 667-683 
    ISSN: 0271-2091
    Keywords: Rotating Flow ; Finite Differences ; Numerical Stability ; 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 computer program has been developed to predict laminar source-sink flow in a rotating cylindrical cavity. Although the program is based on a standard finite difference technique for recirculating flow, it incorporates two novel features. Step changes in grid size are employed to obtain sufficient resolution in the boundary layers and special treatment is given to the solution of the pressure correction equations, in the ‘SIMPLE’ algorithm, in order to improve the convergence properties of the method. Results are presented both for the flow in an infinite rotating cylindrical annulus and a finite rotating cylindrical cavity, with the inner cylindrical surface acting as a uniform source and the outer cylinder as a sink. These show good agreement with existing analytical solutions and illustrate some of the problems associated with the computation of rapidly rotating flows.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 685-699 
    ISSN: 0271-2091
    Keywords: Stokes Flows ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A family of simple Stokes flows involving sliding surfaces adjacent to surfaces at rest is considered. Principally, two specific flow configurations are investigated: (i) that arising when parts of the boundary of an infinitely long circular cylinder are rotating about the axis while other parts of the boundary are at rest, and (ii) the flow produced when a cap of a sphere is held at rest while the remainder of the sphere rotates about the symmetry axis. In each case computer plots of streamlines or constant velocity lines are presented to give a general impression of the resulting flow pattern.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 708-708 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 709-709 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1395-1411 
    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.
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1453-1467 
    ISSN: 0271-2091
    Keywords: Fourier wave theory ; Limit wave ; Stream function ; Truncation order ; 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 review of the analytical and numerical background of Fourier wave theory establishes the commonality of existing formulations and identifies a number of analytical and numerical assumptions that are unnecessary. Some formulations in particular lack flexibility in excluding the possibility of Stokes' second definition of phase speed. A generalized formulation is introduced for comparative purposes and it is shown that published solutions differ only in the approach to the limit wave. Detailed consideration of truncation order confirms that it is the crucial parameter, especially at extreme wave heights. All formulations considered are shown to provide acceptable solutions for small to moderately extreme waves.
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1487-1501 
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    Keywords: Viscoelastic fluid ; Polymer flow ; Velocity correction method ; Two-step explicit scheme ; Pressure boundary condition ; Engineering ; Engineering General
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    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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    International Journal for Numerical Methods in Fluids 4 (1984), S. 765-780 
    ISSN: 0271-2091
    Keywords: Diffraction ; Hydrodynamics ; Ocean Engineering ; Underwater Structures ; Wave Forces ; Offshore Structures ; Velocity Potential ; Boundary Elements ; 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 fluid forces resulting from wave interaction with large submerged structures may be calculated using numerical procedures based on the solution of the associated boundary-value problem. In this paper, the analysis of wave interaction with a fixed submerged object of arbitrary cross-section and infinite length using a two-dimensional boundary value formation based on linear diffraction theory is summarized. Subsequently, the application of the boundary element method to obtain a solution is presented. The numerical considerations are emphasized with particular reference to computational efficiency.Numerical results are presented in the form of dimensionless wave force plots for various structural shapes. In the case of a bottom-seated half cylinder, for which there exists a closed-form solution, comparisons are made between results generated using both boundary element and equivalent finite element approaches. In the case of a submerged cylinder, comparisons are made between boundary element derived values and experimental results. The boundary element results compare well with both the closed-form solution and the experimental values.
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    International Journal for Numerical Methods in Fluids 4 (1984) 
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    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 931-947 
    ISSN: 0271-2091
    Keywords: Two-layer Flow ; Two-step Scheme ; Selective Lumping Method ; Ishikari Bay ; 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 method for the analysis of two-layer density flows is presented in this paper. The standard Galerkin method based on linear interpolation functions is used to yield discrete spatial variables. For numerical integration in time, an explicit two-step selective lumping method is used. Here it is applied to a flow analysis of Ishikari Bay, at the mouth of Ishikari River. This case demonstrates a procedure that yields a numerically stable solution.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 949-969 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Discrete Fourier Transform ; Finite Difference ; Short Convolutions ; No-slip Boundary Condition ; Far Field 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: A mixed discrete Fourier transform-Finite difference algorithm is developed and used for the calculation of rapidly changing viscous fluid flows past a circular cylinder. The numerical approach has been designed to overcome certain difficulties arising for high Reynolds number simulations. The foremost advantage of the technique lies in its fast calculations of the convolution sums portraying the convective terms of the governing equations. Third-order spatial discretizations and fourth-order time marching are implemented.New schemes are proposed for the boundary conditions at the solid wall and at large distances. The techniques are tested on a case study with other schemes (summarized by Roache1) in order to obtain an optimal choice. Definite indications on the stability and accuracy of boundary condition schemes are achieved. Support for the statement of dominant importance of boundary conditions is also given.A comparison of computational results with experimental data is presented for the case study of the flow past an impulsively started cylinder at Reynolds number 20.The time development of the symmetrical zone of recirculation, which is formed at an early stage of the flow, has been studied for 300 ≤ Re ≤ 9500 by means of the proposed algorithm. Computational results, comparisons with experimental data2 and discussion of upper limits of validity of the procedure will be presented in a companion paper.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 997-998 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 999-999 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 989-996 
    ISSN: 0271-2091
    Keywords: Galerkin ; Spline ; Stability ; Disk ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The perturbation equations which characterize the stability of flow over a rotating infinite disk are derived via strict order of magnitude analysis. These equations contain viscous terms not considered by Stuart,1 curvature and Coriolis terms not considered by Brown,2 and axial velocity terms not considered by Kobayashi et al.3 The strategy for reducing the problem to an algebraic system is Galerkin's method with B-spline discretization. In comparison with the Poiseuille flow solutions of Orszag,4 the method is shown to perform well without placing undue demands on computing capability. Critical values of Reynolds number, wave length, vortex orientation and number of spiral vortices calculated by the present method compare favourably with experimental data of Kobayashi et al.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1001-1012 
    ISSN: 0271-2091
    Keywords: Compressible Fluid Flow ; Numerical Analysis ; Pressure Method ; von Kármán Vortex Street ; 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 this paper the pressure method for incompressible fluid flow simulation is extended and applied to the numerical simulation of compressible fluid flow. The governing equations, obtained from the physical principles of conservation of momentum, mass and energy, are first studied from a characteristic point of view. Then they are discretized with a semi-implicit finite difference technique in such a fashion that stability is achieved independently of the speed of sound. The resulting algorithm is fast, accurate and particularly efficient in subsonic flow calculations. As an example, the computer simulation of the von Kármán vortex street is described and discussed.
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 13-23 
    ISSN: 0271-2091
    Keywords: Adaptive Finite Element Method ; Combustion ; 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 adaptive finite element method is developed and applied to study the ozone decomposition laminar flame. The method uses a semidiscrete, linear Galerkin approximation in which the size of the elements is controlled by an integral which minimizes the changes in mesh spacing. The sizes and locations of the elements are controlled by the location and magnitude of the largest temperature gradient. The numerical results obtained with this adaptive finite element method are compared with those obtained using fixed-node finite-difference schemes and an adaptive finite-difference method. It is shown that the adaptive finite element method developed here using 36 elements can yield as accurate flame speeds as fourth-order accurate, fixed-node, finite-difference methods when 272 collocation points are employed in the calculations.
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 71-80 
    ISSN: 0271-2091
    Keywords: Finite Difference ; Residual Method ; Elliptic Equation ; Cavity 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 residual method of finite differencing the governing differential equation for the elliptic transport problem is presented. The new finite differencing technique is applied to (1) the one-dimensional transport problem and (2) the cavity flow problem for numerical illustrations. The results indicate the validity of the residual method of finite differencing. The usual method of term-by-term finite differencing, and considerations such as central differencing, hybrid differencing and upwind differencing are not needed in the present residual method.
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 99-99 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 81-97 
    ISSN: 0271-2091
    Keywords: Compressible Flow ; Turbulent Flow ; Boundary Layers ; Galerkin Method ; Spline Functions ; 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 applicability of a finite element-differential method to the computation of steady two-dimensional low-speed, transonic and supersonic turbulent boundary-layer flows is investigated. The turbulence model chosen for the Reynolds shear stress and turbulent heat flux is the K-∊ two-equation model. Calculations are extended up to the wall and the exact values of the dependent variables at the wall are used as boundary conditions. A number of transformations are carried out and the assumed solutions at a longitudinal station are represented by complete cubic spline functions. In essence, the method converts the governing partial differential equations into a system of ordinary differential equations by a weighted residuals method and invokes an ordinary differential equation solver for the numerical integration of the reduced initial-value problem. The results of the computations reveal that the method is highly accurate and efficient. Furthermore, the accuracy and applicability of the k-∊ turbulence model are examined by comparing results of the computations with experimental data. The agreement is very good.
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 100-100 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 101-114 
    ISSN: 0271-2091
    Keywords: Turbomachines ; Finite Elements ; Transonic 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: This paper describes the extension of a purely two-dimensional finite element method for the calculation of transonic turbomachinery blade-to-blade flows to include the quasi-three-dimensional terms. These terms account for the effect of variations in streamline radius, stream-tube height and blade rotation.By approximating the stream surface as a piecewise linear function, then using a local developed cone transformation on an element basis, the finite element equations are shown to remain of the same form as the two-dimensional equations.The numerical results presented demonstrate that the stream-tube height, streamline radius and blade rotation terms must be included if the prediction of the Mach number distribution around a gas turbine blade is to be calculated correctly.
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 115-132 
    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
    Notes: Steady two-dimensional transonic flow is calculated in cascades of compressor and turbine blades using a mesh of triangular finite elements. A velocity potential is used, the equations being solved by the Newton-Raphson technique. The resulting computer program is fast, and is shown to give good accuracy. Shock waves are well represented, provided they are not too strong.
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 133-154 
    ISSN: 0271-2091
    Keywords: Thermal Convection ; Rotating Channel Flow ; Finite Difference Method ; Secondary Flows ; Rotational Instabilities ; 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 study is conducted on the effect of sidewall heating in the pressure-driven laminar flow of an incompressible viscous fluid through a rectangular channel that is subjected to a spanwise rotation. The time-dependent Navier-Stokes equations are solved along with the conservation equations for energy and mass by a finite-difference technique. The effect of weak to moderate sidewall heating on the overall flow structure at different rotation rates is studied. It is observed that for weak sidewall heating, the secondary flow structure is quite similar to the corresponding isothermal case. However, when the sidewall heating is moderate, various types of secondary flow fields are found to occur depending on the magnitude of the rotation. The influence of rotational speed on the net heat transport for different levels of sidewall heating is also studied. It is found that when the sidewall heating is weak, the basic secondary flow structure for the non-rotating case is of a unicellular form and an increase in the rotation speed leads to an increase in the net heat transfer due mainly to the rotationally driven transport of fluid from the high temperature to the low temperature region. On the other hand, when the sidewall heating is moderate so that the basic secondary flow structure for the non-rotating case has a multicellular configuration, an increase in the rotation speed leads to a decrease in the heat transport due to the weakening of the shear layer near the hot wall.
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  • 88
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 169-189 
    ISSN: 0271-2091
    Keywords: Jeffery-Hamel ; Orr-Sommerfeld ; 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 asymptotic scheme is presented for the solution of the steady state and time dependent stream functions for flows in symmetric curved walled channels. In this scheme a class of non-linear Jeffery-Hamel solutions appear at O(1), and thus provide the first approximation to the steady state stream function. This class of Jeffery-Hamel solutions are evaluated by using a simple perturbation about Poiseuille flow.The classic Orr-Sommerfeld eigenproblem appears at O(1) in the asymptotic development of the time dependent stream function, but here there is a slow streamwise dependence. This eigenvalue problem, for a complex wave number, is solved using an algorithm which automatically provides an initial guess which is then used to iterate to the correct eigenvalue.Higher order terms in the asymptotic development, for both the steady state and time dependent stream functions, are evaluated to provide a solution for the total stream function.
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  • 89
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 155-167 
    ISSN: 0271-2091
    Keywords: Turbulent Flow ; Tri-cusped Duct ; Finite Volume ; 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 orthogonal-cuvilinear-mesh-based finite volume calculation method has been applied to the problem of fully developed turbulent flow in the tri-cusped cornered duct formed when parallel circular rods touch in triangular array. Algebraic stress relations combined with the k-∊ turbulence model are used for calculation of the required stresses. A single circulation of turbulence-driven cross-plane secondary flow from the core into the duct corner has been predicted in a one-sixth symmetry region of the duct and the convective transport effects of this flow are seen to have much influence on local mean flow distributions. The turbulence field predicted by the k-∊ model showed significant damping in the cusped corner region where turbulent viscosities approached the laminar value. Satisfactory agreement was obtained with the limited local and overall mean flow measurements available.
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  • 90
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 331-345 
    ISSN: 0271-2091
    Keywords: Turbomachines ; Design ; Finite Element ; 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 this paper the development of a compatible mixed design and analysis method is presented for the quasi-three-dimensional finite element blade-to-blade program FINSUP. The method consists of two parts. The first is concerned with a method of modelling changes to a blade shape using a surface transpiration model. The second is concerned with determining the relationship between the displaced blade surface and the surface velocity distribution. It is shown that with the Newton-Raphson procedure adopted in the method a very efficient manner of introducing the design option is possible. As a consequence the resulting program is fast and completely interactive. A number of examples are given to illustrate how the mixed design and analysis mode can be used in practical blade design.
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  • 91
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 311-329 
    ISSN: 0271-2091
    Keywords: Cavity Flows ; Finite-differences ; Numerical Accuracy ; Velocity Measurements ; 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 and an experimental study of the flow of an incompressible fluid in a polar cavity is presented. The experiments included flow visualization, in two perpendicular planes, and quantitative measurements of the velocity field by a laser Doppler anemometer. Measurements were done for two ranges of Reynolds numbers; about 60 and about 350. The stream function-vorticity form of the governing equations was approximated by upwind or central finite-differences. Both types of finite-difference approximations were solved by a multi-grid method. Numerical solutions were computed on a sequence of grids and the relative accuracy of the solutions was studied. Our most accurate numerical solutions had an estimated error of 0.1 per cent and 1 per cent for Re = 60 and Re = 350, respectively. It was also noted that the solution to the second order finite difference equations was more accurate, compared to the solution to the first order equations, only if fine enough meshes were used. The possibility of using extrapolations to improve accuracy was also considered. Extrapolated solutions were found to be valid only if solutions computed on fine enough meshes were used. The numerical and the experimental results were found to be in very good agreement.
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  • 92
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 347-356 
    ISSN: 0271-2091
    Keywords: Aerofoils ; Unsteady ; Potential ; Discrete ; Vortex ; Two-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 new model is presented for the calculation of the incompressible, inviscid flow around an arbitrary aerofoil undergoing unsteady motion. The technique was developed from the steady flow algorithm of Leishman and Galbraith1 in which use was made of a linear distribution of panel vorticity. The procedure is in the same class as that of Basu and Hancock2 but, because of the particular approach to the manner of specifying the shed vorticity, only a set of linear simultaneous equations needs be solved, unlike the method of Reference 2, complicated by the necessary solution of a quadratic.A brief history of unsteady flow modelling is given in the introduction, followed by the mathematical details of the current method. Results are presented and discussed for a number of cases which clearly illustrate relevant characteristics of unsteady flow.
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  • 93
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 357-380 
    ISSN: 0271-2091
    Keywords: Iterative Methods ; Implicit Procedures ; 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 general implicit (GI) method for solving iteratively the algebraic system arising from a finite difference approximation of an elliptic partial differential equation is formulated. Under certain assumptions this method can be reduced to the already known implicit techniques. It is shown that the GI method has a very special physical meaning when solving fluid flow problems. It is shown also how this method can be optimized to achieve the maximum rate of convergence. Finally it is shown how this new strategy is applied by solving some classical numerical fluid dynamics problems.
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  • 94
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 399-401 
    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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  • 95
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 381-391 
    ISSN: 0271-2091
    Keywords: Matrix Iterative Methods ; Strongly Implicit Procedure ; 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 solving elliptic difference equations is derived based on the strongly implicit method. This parametrized strongly implicit method has three free parameters which may be functions of the field's nodal point. The method has some resemblance to the SOR techniques, but in the present method the off-diagonal entries are also over-relaxed. The main application of this method is for transport equations such as those governing the fluid flow and heat transfer fields.
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  • 96
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 393-397 
    ISSN: 0271-2091
    Keywords: Shallow-Water Equations ; Spurious Solutions ; Numerical Boundary Condition ; Advection ; 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 simple explanation is given of the occurrence of wiggles in the flow field near outflow boundaries. If the shallow-water equations are solved numerically spurious solutions with an oscillatory character turn out to exist, which can be generated by certain additional numerical boundary conditions on the downstream side. The wiggles usually damp quickly with the distance from the boundary. Some ways of handling the downstream boundary are given which largely avoid the occurrence of wiggles.
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  • 97
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 402-403 
    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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  • 98
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985) 
    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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  • 99
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 439-442 
    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
    Additional Material: 2 Ill.
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  • 100
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 405-425 
    ISSN: 0271-2091
    Keywords: DuFort-Frankel ; Saul'ev ; Instability ; Sea Model ; Hydrodynamic ; Three-dimensional Time-splitting ; 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 three dimensional hydrodynamic sea model of an arbitrary sea area is formulated using sigma co-ordinates in the vertical. The solution of the equations using finite difference grids in the horizontal and the vertical is described.Discretization of the vertical viscosity term in the hydrodynamic equations using the DuFort-Frankel and Saul'ev methods is developed. Some numerical instabilities occur with the DuFort-Frankel method which can be overcome by splitting the hydrodynamic equations into equations describing the mean flow and equations describing the deviations from it. The computational advantages of solving these equations with different time steps are discussed.The accuracy and stability of the various methods is demonstrated for wind induced flow in a simple rectangular basin having dimensions representing the North Sea.
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