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A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients. (English) Zbl 1094.76546
Summary: A class of higher order compact (HOC) schemes has been developed with weighted time discretization for the two-dimensional unsteady convection-diffusion equation with variable convection coefficients. The schemes are second or lower order accurate in time depending on the choice of the weighted average parameter \(\mu\) and fourth order accurate in space. For \(0.5\leq \mu\leq1 \), the schemes are unconditionally stable. Unlike usual HOC schemes, these schemes are capable of using a grid aspect ratio other than unity. They efficiently capture both transient and steady solutions of linear and nonlinear convection-diffusion equations with Dirichlet as well as Neumann boundary condition. They are applied to one linear convection-diffusion problem and three flows of varying complexities governed by the two-dimensional incompressible Navier-Stokes equations. Results obtained are in excellent agreement with analytical and established numerical results. Overall the schemes are found to be robust, efficient and accurate.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76R99 Diffusion and convection
76D05 Navier-Stokes equations for incompressible viscous fluids
Software:
KELLEY
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[1] Computational Fluid Mechanics and Heat Transfer. Hemisphere Publishing Corporation: New York, 1984. · Zbl 0569.76001
[2] Computational Fluid Dynamics. McGraw-Hill, Inc.: New York, 1995. · Zbl 0865.76002
[3] Numerical Solution of Partial Differential Equations: Finite Difference Methods. Clarendon Press: Oxford, 1984.
[4] Mackinnon, Journal of Computational Physics 75 pp 151– (1988) · Zbl 0632.76110
[5] Mackinnon, International Journal for Numerical Methods in Fluids 13 pp 739– (1991) · Zbl 0729.76611
[6] Spotz, International Journal for Numerical Methods in Engineering 38 pp 3497– (1995) · Zbl 0836.76065
[7] Hirsh, Journal of Computational Physics 9 pp 90– (1975) · Zbl 0326.76024
[8] Rai, Journal of Computational Physics 96 pp 15– (1991) · Zbl 0726.76072
[9] Lele, Journal of Computational Physics 103 pp 16– (1992) · Zbl 0759.65006
[10] Abarbanel, Journal of Scientific Computing 3 pp 275– (1988) · Zbl 0667.76102
[11] Balzano, International Journal for Numerical Methods in Fluids 31 pp 481– (1999) · Zbl 0952.76052
[12] Noye, International Journal for Numerical Methods in Engineering 26 pp 1615– (1988) · Zbl 0638.76104
[13] Noye, International Journal for Numerical Methods in Fluids 9 pp 75– (1989) · Zbl 0658.76079
[14] High order compact finite difference schemes for computational mechanics. PhD thesis, University of Texas at Austin, December, 1995.
[15] Strikwerda, International Journal for Numerical Methods in Fluids 24 pp 715– (1997) · Zbl 0889.76050
[16] Yanwen, International Journal for Numerical Methods in Fluids 30 pp 509– (1999) · Zbl 0946.76062
[17] Chen, International Journal for Numerical Methods in Fluids 31 pp 747– (1999) · Zbl 0952.76043
[18] Higher order discretization of initial boundary value problems for mixed systems. In Proceedings Seminar für Angewandte Mathematik, ETH-Zurick, number 96-05, May 1996.
[19] Iterative Methods for Linear and Nonlinear Equations. SIAM Publications: Philadelphia, 1995.
[20] Sleijpen, Computational Fluid Dynamics Review pp 457– (1995)
[21] Chorin, Mathematics of Computation 22 pp 747– (1968)
[22] Ghia, Journal of Computational Physics 48 pp 387– (1982) · Zbl 0511.76031
[23] Spotz, International Journal for Numerical Methods in Fluids 28 pp 737– (1998) · Zbl 0930.76059
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