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  • Articles  (13)
  • Finite difference  (13)
  • Wiley-Blackwell  (13)
  • Annual Reviews
  • 1990-1994  (13)
  • 1980-1984
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (13)
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  • Articles  (13)
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  • Wiley-Blackwell  (13)
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (13)
  • 1
    Electronic Resource
    Electronic Resource
    Acceleration of convergence by shifting the spectrum of implicit finite difference operators associated with the equations of gas dynamics (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 443-462 
    Details
    ISSN: 0271-2091
    Keywords: Acceleration of convergence ; Steady state solution ; Finite difference ; Eigensystem analysis ; Shifting of the spectrum ; Euler equations ; Iterative method ; Frechet derivative ; Eigenvalue annihilation ; Rates of convergence ; 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: Eigensystem analysis techniques are applied to finite difference formulations of the Navier-Stokes equations in one dimension. Spectra of the resulting implicit difference operators are computed. The largest eigenvalues are calculated by using a combination of the Frechet derivative of the operators and Arnoldi's method. The accuracy of Arnoldi's method is tested by comparing the rate of convergence of the iterative method with the dominant eigenvalue of the original iteration matrix.On the basis of the pattern of eigenvalue distributions for various flow configurations, a shifting of the implicit operators in question is devised. The idea of shifting is based on the power method of linear algebra and is very simple to implement. This procedure has improved the rates of convergence of CFD codes (developed at NASA Ames Research Center) by 20%-50%. The sensitivity of the computed solution with respect to the shift is also studied. Finally, an adaptive shifting of the spectrum together with Wynn's acceleration algorithm are discussed. It turns out that the shifting process is a preconditioner for Wynn's method.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120503
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  • 2
    Electronic Resource
    Electronic Resource
    A study of upstream-weighted high-order differencing for approximation to flow convection (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 167-199 
    Details
    ISSN: 0271-2091
    Keywords: Finite difference ; High-order schemes ; Numerical diffusion ; Solution unboundedness ; 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 a number of upstream-weighted second- and third-order difference schemes. Also considered are the conventional upwind and central difference schemes for comparison. It commences with a general difference equation which unifies all the given first-, second- and third-order schemes. The various schemes are evaluated through the use of the general equation. The unboundedness and accuracy of the solutions by the difference schemes are assessed via various analyses: examination of the coefficients of the difference equation, Taylor series truncation error analysis, study of the upstream connection to numerical diffusion, single-cell analysis. Finally, the difference schemes are tested on one- and two-dimensional model problems. It is shown that the high-order schemes suffer less from the problem of numerical diffusion than the first-order upwind difference scheme. However, unboundedness cannot be avoided in the solutions by these schemes. Among them the linear upwind difference scheme presents the best compromise between numerical diffusion and solution unboundedness.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130204
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  • 3
    Electronic Resource
    Electronic Resource
    Surface tension and buoyancy-driven flow in a non-isothermal liquid bridge (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 197-215 
    Details
    ISSN: 0271-2091
    Keywords: Thermocapillary flow ; Buoyancy ; Free surface ; Finite difference ; Picard iteration ; ADI ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Navier-Stokes-Boussinesq equations governing the transport of momentum, mass and heat in a non-isothermal liquid bridge with a temperature-dependent surface tension are solved using a vorticity-stream-function formulation together with a non-orthogonal co-ordinate transformation. The equations are discretized using a pseudo-unsteady semi-implicit finite difference scheme and are solved by the ADI method. A Picard-type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary-driven flow situations and mixed thermocapillary- and bouyancy-driven flow.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140207
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  • 4
    Electronic Resource
    Electronic Resource
    An improved SIP scheme for numerical solutions of transonic streamfunction equations (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 591-602 
    Details
    ISSN: 0271-2091
    Keywords: Shock capturing ; Streamfunction equation ; SIP scheme ; Finite difference ; Transonic cascade flow ; Comparison with experiment ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new improved strongly implicit procedure (SIP) is presented for solving large sets of transonic streamfunction equations with matrix of coefficients [B]. This algorithm has several advantages over those now in use. First, Stone's auxiliary matrix [B′] is non-symmetric, while in the present scheme the auxiliary matrix [B′] is symmetric and the matrix [B + B′] is positive definite and symmetric when [B] is a symmetric matrix. This ensures the numerical stability of the iterative algorithms. Secondly, for an appropriate choice of iterative parameter ω, the rate of convergence of the new iterative procedure should be faster than the original SIP scheme.Numerical results of the blade-to-blade flows are given with the present scheme. It is shown that the algorithm is efficient and robust.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100506
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  • 5
    Electronic Resource
    Electronic Resource
    On the numerical solution of the turbulence energy equations for wave and tidal flows (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 17-41 
    Details
    ISSN: 0271-2091
    Keywords: Finite difference ; Hydrodynamic ; Turbulence energy ; Tidal ; Wind 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: This paper deals with the numerical solution, using finite difference methods, of the hydrodynamic and turbulence energy equations which describe wind wave and tidally induced flow.Calculations are performed using staggered and non-staggered finite difference grids in the vertical, with various time discretizations of the production and dissipation terms in the turbulence energy equations. It is shown that the time discretization of these terms can significantly influence the stability of the solution. The effect of time filtering on the numerical stability of the solution is also considered. The form of the mixing length is shown to significantly influence the bed stress in wind wave problems.A no-slip condition is applied at the sea bed, and the associated high-shear bottom boundary layer is resolved by transforming the equations onto a logarithmic or log-linear co-ordinate system before applying the finite difference scheme.A computationally economic method is developed which remains stable even when a very fine vertical grid (over 200 points) is used with a time step of up to 30 min.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120103
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  • 6
    Electronic Resource
    Electronic Resource
    An application of the vorticity-vector potential method to laminar cube flow (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 875-888 
    Details
    ISSN: 0271-2091
    Keywords: 3D Incompressible laminar flow ; Cube Vorticity-vector potential formulation ; Finite difference ; Vorticity transport equation ; Poisson equations SOR algorithm ; 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: Three-dimensional incompressible laminar flow around a cube is investigated using the vorticity-vector potential formulation of the equations of motion. Numerical solutions to á semi-implicit finite difference approximation to the vorticity transport equation coupled to discrete Poisson equations for the scalar and vector potentials are obtained using an eight-colour SOR algorithm. Calculations are done at a range of Reynolds numbers from 10 to 100. The predicted drag and other flow characteristics are found to agree well with experimental results, including those from a cube drop experiment performed for the present study.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100803
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  • 7
    Electronic Resource
    Electronic Resource
    On the accuracy of finite difference and modal methods for computing tidal and wind wave current profiles (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 101-124 
    Details
    ISSN: 0271-2091
    Keywords: Finite difference ; Spectral ; Tidal wave ; Wind wave ; Crank-Nicolson ; Logarithmic transform ; 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 deals with the comparative accuracy of using finite difference grids or a modal representation through the vertical in modelling tidally or wind wave induced current profiles.A point model is used in the vertical, with a no-slip condition at the sea bed. In the finite difference approach the high-shear bottom layer is resolved using either a regular grid on a logarithmic or log-linear transformed co-ordinate or an irregular grid, varying in such a manner as to retain second-order accuracy. The accuracy of these various grid schemes is considered in detail.The relative merits of using either the Crank-Nicolson or Dufort-Frankel time integration methods are considered; in the case of a fine grid in a high-viscosity region, some numerical problems are found with the Dufort-Frankel method.An alternative approach to using a finite difference grid in the vertical, namely a modal (spectral) method, is described. The form of the modes is such that they can accurately resolve the high-shear bottom boundary layer.Calculations show that the thickness of the bottom boundary layer in relation to the total water depth is important in determining the choice of grid transform and rates of convergence of solutions using finite difference or modal methods. However, for the majority of problems the modal solution is numerically attractive owing to its computational efficiency and the ease with which solution algorithms based upon it can be coded in vectorizable form suitable for the new generation of vector computers.The influence of viscosity profile, its time variation and water depth upon tidally induced or wave induced currents is considered. Calculations suggest that near-bed measurements of tidal flow in shallow water together with associated modelling would enable appropriate formulations of eddy viscosity to be determined. Similar measurements, though using a laboratory flume, would be appropriate for wind wave problems.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120202
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  • 8
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    Electronic Resource
    A control volume finite difference method for buoyant flow in three-dimensional curvilinear non-orthogonal co-ordinates (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 199-211 
    Details
    ISSN: 0271-2091
    Keywords: Finite difference ; Natural convection ; Enclosure flow ; Non-orthogonal 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: This paper presents a control-volume-based finite difference method in non-orthogonal curvilinear coordinates on a local basis in which the vectors and tensors are all based on the general curvilinear coordinates for buoyant flow calculations in arbitrary three-dimensional geometries. The governing equations are transformed from Cartesian co-ordinates into generalized curvilinear co-ordinates. After integrating the set of equations for the control volumes, the finite difference equations are then formulated by a proper treatment of the heat flux and stress tensors and by incorporating the QUICK scheme for the convective terms. The solution procedure then follows the one for three-dimensional Cartesian co-ordinates.Examples are given in problems of natural convection in such three-dimensional enclosures as parallelepiped enclosures and horizontal closed cylinders with differentially heated ends. In the latter case, important applications have been found in crystal growth by means of chemical vapour deposition in a cylindrical ampoule, in which uniform heat fluxes along the two ends are required in order to produce high-quality crystals. Special attention is given to the insertion of baffles in the cylinder to improve the recirculating flow patterns near the two ends.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100206
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  • 9
    Electronic Resource
    Electronic Resource
    A stable high-order method for the heated cavity problem (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 1313-1332 
    Details
    ISSN: 0271-2091
    Keywords: A fourth-order method ; Navier-Stokes equation ; Stability ; Finite difference ; 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 fourth-order method, without using extrapolation, is developed for the steady-state solution of a non-linear system of three simultaneous partial differential equations for the flow of a fluid in a heated closed cavity. The method is a finite difference method which has converged for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. The results are presented and compared with some of the accurate results available in de Vahl Davis and Jones, Shay and Schultz, and Dennis and Hudson. The method used to develop the fourth-order method presented in this paper can be used to develop high-order methods for other partial differential equations. The method was developed to be stable without using the upwinding technique.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650151106
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  • 10
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    Modelling the non-linear interaction of wind and tide: Its influence on current profiles (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 163-188 
    Details
    ISSN: 0271-2091
    Keywords: Non-linear interaction ; Hydrodynamic ; Spectral ; Finite difference ; Tidal current ; Wind-driven current ; 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 single-point model in the vertical is used to examine the coupling between tidal currents and wind-driven flows in shallow near-coastal regions. Calculations using both a linear slip and a no-slip condition at the sea bed clearly show that coupling between tidal and wind-driven currents cannot occur in a linear model with a time-independent eddy viscosity. However with a physically more realistic time-varying viscosity related to the flow field, coupling does occur, the magnitude of this non-linear interaction depending upon the change in eddy viscosity over a tidal cycle and the intensity of shear in the vertical. A point model in the vertical with flow induced by an oscillatory pressure gradient and an additional constant wind stress is used to examine the influence of viscosity parametrization and water depth upon this coupling.The solution in the vertical is accomplished using both a functional approach and a finite difference method. Some conclusions as to the relative merits of these approaches, particularly the use of a transformed grid in the case of high-shear surface and bed boundary layers, are made in the paper.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180203
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  • 11
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    Simulation of three-dimensional unsteady viscous free surface flow around a ship model (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 321-342 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Free surface flow ; Finite difference ; Wave resistance ; Frictional resistance ; Adaptive mesh ; 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 present here a numerical method for solving the free surface flow around a ship at forward speed in calm water. The fluid is assumed to be Newtonian and the Reynolds-averaged Navier-Stokes equations are solved by a finite difference method. Modelization of turbulence is achieved by the algebraic model proposed by Baldwin and Lomax. Fully non-linear free surface conditions are satisfied in the model and a method to avoid the incompatibility between free surface conditions and no-slip conditions at the waterline is proposed. Numerical results obtained for a Wigley hull are compared with experimental results.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650190404
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  • 12
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    Efficient higher-order backward characteristics schemes for transient advection (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 997-1012 
    Details
    ISSN: 0271-2091
    Keywords: Advection ; Method of characteristics ; Finite difference ; Flux limiter ; 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 use of the highest-order ((N - 1)th-order) Lagrangian interpolation Polynomial for the approximation of the exact solution in the backward characteristics scheme with N nodes is inefficient owing to the excessive number of terms in the polynomial. New schemes based on a combination of lower-order polynomials to approximate the exact solution are developed, with the relative weighting of the polynomials determined by Fourier mode analysis. With the addition of a flux limiter and a modified discriminator, the resulting schemes are oscillation-free, highly accurate, efficient and more cost-effective as compared with those schemes using the highest-order Lagrangian polynomial.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650191104
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  • 13
    Electronic Resource
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    Modelling the initial motion of large cylindrical and spherical bubbles (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 109-129 
    Details
    ISSN: 0271-2091
    Keywords: Bubbles ; Finite difference ; Initial motion ; 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 two-dimensional, transient, finite difference technique based on a volume fraction specification of the free surface position and accounting for the effects of surface tension is shown to accurately predict the initial motion of large cylindrical and spherical bubbles. The predictions compare very favourably with the experimental data of Walters and Davidson. The initial acceleration of cylindrical and spherical bubbles is properly predicted as g and 2g respectively. The penetration of a tongue of liquid from below is the dominant process by which large deformations from the original shape take place and is well predicted by the model in both cases. For the spherical case the eventual transition into a toroidal bubble is demonstrated and the circulation associated with a rising toroidal bubble as a function of its volume upon release is shown to agree very well with experiments. Iterative linear equation-solving techniques applicable to the special nature of the linear system resulting from such a free surface specification are surveyed and a simple Jacobi iteration based on red-black ordering is found to perform well. The impact of the free surface on the relaxation of the linear system and the convergence criteria is also explored.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130107
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