A Multigrid Semi-implicit Line-Method for Viscous Incompressible and Low-Mach-Number Flows on High Aspect Ratio Grids

Journal of Computational Physics

Volumn 154, Issue 2, 1999, Pages 310-341

  Vierendeels, Jan ^a   Riemslagh, Kris ^a   Dick, Erik ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

High aspect ratio grid; Multigrid method; Preconditioning; Viscous incompressible flow; Viscous low Mach number flow

Indexed keywords

ACCELERATION; AERODYNAMICS; ASPECT RATIO; DISCRETE EVENT SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; INCOMPRESSIBLE FLOW;

DISCRETIZATIONS; HIGH ASPECT RATIO GRID; LINE METHODS; LOW-MACH-NUMBER FLOW; MULTIGRID METHODS; MULTIGRIDS; PRECONDITIONING; SEMI-IMPLICIT; VISCOUS INCOMPRESSIBLE FLOWS; VISCOUS LOW-MACH-NUMBER FLOW;

MACH NUMBER;

EID: 0001349565     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6315     Document Type: Article

References (18)

1. D. R. Chenoweth and S. Paolucci, Natural convection in an enclosed vertical air layer with large horizontal temperature differences, J. Fluid. Mech. 169, 173 (1986).
2. Y. Choi and C. Merkle, The application of preconditioning in viscous flows, J. Comput. Phys. 105, 207 (1993).
3. A. J. Chorin, A numerical method for solving incompressible viscous flow problems, AIAA J. 2, 12 (1967).
4. D. L. Darmofal and B. van Leer, Local preconditioning: Manipulating mother nature to fool father time, in Computing the Future. II. Computational Fluid Dynamics and Transonic Flow, edited by D. Caughey and M. Hafez (Wiley, New York, 1998).
5. E. Dick and J. Linden, A multigrid method for steady incompressible Navier-Stokes equations based on flux difference splitting, Int. J. Numer. Methods Fluids 14, 1311 (1992).
6. J. Edwards and M.-S. Liou, Low-diffusion flux splitting methods for flows at all speeds, AIAA J. 36(9), 1610 (1998).
7. A. Godfrey, R. Walters, and B. van Leer, Preconditioning for the Navier-Stokes equations with finite rate chemistry, in Proc. 31st Aerospace Sciences Meeting, Reno, 1993, AIAA-93-0535.
8. B. Koren and B. van Leer, Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions, Adv. Comput. Math. 4, 127 (1995).
9. D. Lee, B. van Leer, and J. Lynn, A local Navier-Stokes preconditioner for all Mach and cell Reynolds numbers, in Proc. 13th AIAA CFD Conference, Snowmass, CO (AIAA, Washington, DC, 1997), AIAA-97-2024, p. 842.
10. W. Lee, "Local Preconditioning of the Euler Equations," Ph.D. thesis, University of Michigan, 1991.
11. M.-S. Liou and C. J. Steffen, Jr., A new flux splitting scheme, J. Comput. Phys. 107, 23 (1993).
12. D. J. Mavriplis, Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes, in Proc. 13th AIAA CFD Conference, Snowmass, CO (AIAA, Washington, DC, 1997), AIAA-97-1952, p. 659.
13. C. L. Merkle, J. Y. Sullivan, P. E. O. Buelow, and S. Venkateswaran, Computation of flows with arbitrary equations of state, AIAA J. 36(4), 515 (1998).
14. E. Morgan, J. Periaux, and F. Thomasset, Analysis of laminar flow over a backward facing step, in Notes on Numerical Fluid Mechanics (Vieweg, Braunschweig, 1984), Vol. 9.
15. E. Turkel, A review of preconditioning methods for fluid dynamics, Appl. Numer. Math. 12, 257 (1993).
16. E. Turkel, Preconditional techniques in computational fluid dynamics, Annu. Rev. Fluid Mech. 31, 385 (1999).
17. J. Weiss and W. Smith, Preconditioning applied to variable and constant density flows, AIAA J. 33(11), 2050 (1995).
18. F. M. White, Viscous Fluid Flow (McGraw-Hill, New York, 1974).