A fast poisson solver for the finite difference solution of the incompressible Navier-Stokes equations

SIAM Journal on Scientific Computing

Volumn 19, Issue 5, 1998, Pages 1606-1624

  Golub, Gene H ^a   Huang, Lan Chieh ^b   Simon, Horst ^c   Tang, Wei Pai ^d  

^a Stanford University   (United States)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Fast solver; Generalized eigenvalues; Incompressible Navier Stokes equations; Poisson equation

Indexed keywords

EID: 0007319408     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595285299     Document Type: Article

References (24)

1. J. B. BELL, P. COLELLA, AND H. M. GLAZ, A second-order projection method for the incom-pressible Navier-Stokes equations, J. Comput. Phys., 85 (1989), pp. 257-283.
2. B. BUZBEE, G. GOLUB, AND C. NILSON, On direct methods for solving Poisson's equation, SIAM J. Numer. Anal., 7 (1970), pp. 627-656.
3. C. CANUTO, M. Y. HUSSAINI, A. QUARTERONI, AND T. A. ZANG, Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1987.
4. A. J. CHORIN, Numerical solution of Navier-Stokes equations, Math. Comp., 22 (1968), pp. 745-762.
5. C. R. CRAWFORD, Reduction of aa band-symmetric generalized eigenvalue problem, Comm. ACM., 16 (1973), pp. 41-44.
6. M. FORTIN, R. PEYRET, AND R. TEMAM, Calcul des ecoulements d'un fluide visqueux incompressible, J. Mec., 10 (1971), pp. 357-390.
7. U. GHIA, K. N. GHIA, AND C. T. SHIN, High-resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48 (1982), pp. 387-411.
8. G. GOLUB AND C. VAN LOAN, Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, MD, 1989.
9. R. G. GRIMES, J. G. LEWIS, AND H. D. SIMON, A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 228-272.
10. L. C. HUANG, J. OLIGER, W.-P. TANG, AND Y. D. WU, Toward efficient and robust finite difference schemes for unsteady incompressible Navier-Stokes equation on the half-staggered mesh, in Proc. 6th International Symposium on CFD, 1995.
11. L. C. HUANG, On boundary treatment for the numerical solution of the incompressible Navier-Stokes equations with finite difference methods, J. Comput. Math, 14 (1996) pp. 135-142.
12. L. C. HUANG AND Y. D. WU, On the half-staggered mesh for the finite difference solution of the unsteady incompressible Navier-Stokes equations, J. Comput. Math, 18 (1996), pp. 24-37. (in Chinese).
13. L. C. HUANG AND Y. D. WU, The component-consistent pressure correction projection method for the incompressible Navier-Stokes equations, Comput. Math. Appl., 31 (1996), pp. 1-21.
14. L. KAUFMAN, An algorithm for the banded symmetric generalized matrix eigenvalue problem, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 372-389.
15. L. KAUFMAN AND D. D. WARNER, High-order, fast-direct methods for separable elliptic equations, SIAM J. Numer. Anal., 21 (1984), pp. 672-694.
16. C. B. MOLER AND G. W. STEWART, An algorithm for generalized matrix eigenvalue problems, SIAM J. Numer. Anal., 10 (1973), pp. 241-256.
17. R. PEYRET AND T. D. TAYLOR, Computational Methods for Fluid Flow, Springer-Verlag, New York, 1983.
18. R. L. SANI, The cause and cure of the spurious pressure generated by certain FEM solution of the incompressible Navier-Stokes equations: Part I, Internat. J. Numer. Methods Fluids, 1 (1981), pp. 17-43.
19. U. SCHMANN AND R. SWEET, A direct method for the solution of Poisson's equation with Neumann boundary conditions on a staggered grid of arbitrary sizes, J. Comput. Phys., 20 (1976), pp. 171-182.
20. SHYY AND VU, On the adoption of velocity variable and grid system for fluid flow computation in curvilinear coordinates, J. Comput. Phys., 92 (1991), pp. 82-105.
21. A. B. STEPHEN, A finite difference Galerkin formulation for the incompressible Navier-Stokes equations, J. Comput. Phys., 53 (1984), pp. 152-172.
22. G. W. STEWART, On the perturbation of pseudo-inverses, projections, and linear least squares problems, SIAM Rev., 19 (1977), pp. 634-662.
23. R. TEMAM, Navier-Stokes Equations, Theory and Numerical Analysis, Elsevier Science Pub. B. V., New York, 1984.
24. S. WANG AND S. ZHAO, An algorithm for Ax = λBx with symmetric and positive definite a and b, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 654-660.