High accuracy multigrid solution of the 3D convection-diffusion equation

Applied Mathematics and Computation

Volumn 113, Issue 2, 2000, Pages 249-274

  Gupta, Murli M ^a   Zhang, Jun ^b  

^a GEORGE WASHINGTON UNIVERSITY   (United States)

^b UNIVERSITY OF KENTUCKY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; FOURIER TRANSFORMS; MATHEMATICAL OPERATORS; RELAXATION PROCESSES; REYNOLDS NUMBER; THERMAL DIFFUSION IN SOLIDS;

GAUSS-SEIDEL RELAXATION; HIGH ACCURACY MULTIGRID METHOD; MULTIGRID INTER-GRID TRANSFER OPERATORS; THREE-DIMENSIONAL CONVECTION-DIFFUSION EQUATIONS;

HEAT CONVECTION;

EID: 0034225299     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(99)00085-5     Document Type: Article

References (25)

1. Ananthakrishnaiah U., Manohar R., Stephenson J.W. Fourth-order finite difference methods for three-dimensional general linear elliptic problems with variable coefficients. Numer. Methods Partial Differential Equations. 3:1987;229-240.
2. V.A. Bandy, Black box multigrid for convection-diffusion equations on advanced computers, Ph.D. Thesis, University of Colorado at Denver, 1996.
3. Behie A., Forsyth P.A. Jr. Multi-grid solution of three dimensional problems with discontinuous coefficients. Appl. Math. Comput. 13:1983;229-240.
4. 2-norm. SIAM J. Numer. Anal. 31:1994;1695-1730.
5. Brandt A., Yavneh I. Inadequency of first-order upwind difference schemes for some recirculating flows. J. Comput. Phys. 93:1991;128-143.
6. Brandt A., Yavneh I. On multigrid solution of high-Reynolds incompressible entering flows. J. Comput. Phys. 101:1992;151-164.
7. Brandt A., Yavneh I. Accelerated multigrid convergence and high-Reynolds recirculating flows. SIAM J. Sci. Comput. 14:1993;607-626.
8. Dendy J.E. Jr. Two multigrid methods for three-dimensional equations with highly discontinuous coefficients. SIAM J. Sci. Statist. Comput. 8:1987;673-685.
9. 4 finite-difference approximations to operators of Navier-Stokes type. J. Comput. Phys. 85:1989;390-416.
10. Gary J., McCormick S., Sweet R. Successive overrelaxation, multigrid, and preconditioned conjugate gradient algorithms for solving a diffusion problem on a vector computer. Appl. Math. Comput. 13:1983;285-309.
11. C. Greif, J.M. Varah, Iterative solution of cyclically reduced systems arising from discretization of the three dimensional convection-diffusion equation, SIAM J. Sci. Comput. (to appear).
12. Gupta M.M., Kouatchou J. Symbolic derivation of finite difference approximations for three dimensional Poisson equation. Numer. Methods Partial Differential Equations. 14:1998;593-606.
13. Gupta M.M., Manohar R.P., Stephenson J.W. A single cell high order scheme for the convection-diffusion equation with variable coefficients. Int. J. Numer. Methods Fluids. 4:1984;641-651.
14. Gupta M.M., Manohar R.P., Stephenson J.W. High-order difference schemes for two-dimensional elliptic equations. Numer. Methods Partial Differential Equations. 1:1985;71-80.
15. Gupta M.M., Kouatchou J., Zhang J. A fourth order compact solver for convection-diffusion equations. J. Comput. Phys. 132:1997;226-232.
16. W.H. Holter, A vectorized multigrid solver for the three dimensional Poisson equation, in: A.H.L. Emmen (Ed.), Supercomputer Applications, North-Holland, Amsterdam, 1985, pp. 17-32.
17. Li M., Tang T., Fornberg B. A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids. 20:1995;1137-1151.
18. Y. Saad, J. Zhang, BILUM: block versions of multi-elimination and multi-level ILU preconditioner for general sparse linear systems, SIAM J. Sci. Comput. (to appear).
19. Spotz W.F., Carey G.F. Formulation and experiments with high-order compact schemes for nonuniform grids, Int. J. Numer. Methods Heat Fluid Flow. 8(3):1998;288-303.
20. C.-A. Thole, U. Trottenberg, Basic smoothing procedures for the multigrid treatment of elliptic 3D-operator, in: D. Braess, W. Hackbusch, U. Trottenberg, (Eds.), Advances in Multi-Grid Methods, Notes on Numerical Fluid Mechanics, vol. 11, Vieweg, Braunschweig, 1985, pp. 102-111.
21. P. Wesseling, An Introduction to Multigrid Methods, Wiley, Chichester, 1992.
22. Zhang J. A cost-effective multigrid projection operator. J. Comput. Appl. Math. 76:1996;325-333.
23. Zhang J. Accelerated high accuracy multigrid solution of the convection-diffusion equation with high Reynolds number. Numer. Methods Partial Differential Equations. 77:1997;73-89.
24. Zhang J. Residual scaling techniques in multigrid. II: Practical applications. Appl. Math. Comput. 90:1998;229-252.
25. Zhang J. On convergence and performance of iterative methods with fourth-order compact schemes. Numer. Methods Partial Differential Equations. 14:1998;263-280.