Efficient solution of the steady-state Navier-Stokes equations using a multigrid preconditioned Newton-Krylov method

International Journal for Numerical Methods in Fluids

Volumn 43, Issue 12, 2003, Pages 1407-1427

  Syamsudhuha, ^a   Silvester, David J ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Krylov; Multigrid; Navier Stokes; Newton; Non linear

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; LINEARIZATION; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER;

MULTIGRID CYCLES;

FLOW OF FLUIDS;

COMPUTATIONAL FLUID DYNAMICS; DIFFUSION-CONVECTION THEORY; FLUID DYNAMICS; NAVIER-STOKES EQUATIONS; REYNOLDS NUMBER;

EID: 0346421321     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.627     Document Type: Article

References (19)

1. Engelman MS, Strang G, Bathe KJ. The application of quasi-Newton methods in fluid mechanics. International Journal for Numerical Methods in Engineering 1981; 17:707-718.
2. Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48:387-411.
3. McHugh PR, Knoll DA. Fully coupled finite volume solutions of the incompressible Navier Stokes and energy equations using an inexact Newton method. International Journal for Numerical Methods in Fluids 1994; 19:439-455.
4. Knoll DA, Rider WJ. A multigrid preconditioned Newton-Krylov method. SIAM Journal on Scientific Computing 1999; 21:691-710.
5. Kay D, Loghin D, Wathen AJ. A preconditioner for the steady state Navier-Stokes equations. SIAM Journal on Scientific Computing 2002; 24:237-256.
6. Silvester DJ, Elman HC, Kay D, Wathen A. Efficient preconditioning of the linearized Navier-Stokes equations. Journal of Computational and Applied Mathematics 2001; 128:261-279.
7. Elman HC. Preconditioning for the steady-state Navier-Stokes equations with low viscosity. SIAM Journal on Scientific Computing 1999; 20:1299-1316.
8. Girault V, Raviart PA. Finite Element Methods for Navier-Stokes Equations-Theory and Algorithms. Springer: Berlin, 1986.
9. Eisenstat SC, Walker HF. Choosing the forcing terms in an inexact Newton method. SIAM Journal on Scientific Computing 1996; 17:16-32.
10. Kelley CT. Iterative Methods for Linear and Nonlinear Equations. SIAM: Philadelphia, 1995.
11. Murphy MF, Golub GH, Wathen AJ. A note on preconditioning for indefinite linear systems. SIAM Journal on Scientific Computing 2000; 21:1969-1972.
12. Gunzburger MD. Navier-Stokes equations for incompressible flows: finite element methods. Handbook of Computational Fluid Mechanics. Academic Press: London, 1996.
13. Gunzburger MD. Finite Element Methods for Viscous Incompressible Flows. Academic Press: London, 1989.
14. Ramage A. A multigrid preconditioner for stabilised discretizations of advection-diffusion problems. Journal of Computational and Applied Mathematics 1999; 101:187-203.
15. Layton W, Lee HK, Peterson J. Numerical solution of the stationary Navier-Stokes equations using a multilevel finite element method. SIAM Journal on Scientific Computing 1998; 20:1-12.
16. Pernice M, Wolker HF. NITSOL: A Newton iterative solver for nonlinear system. SIAM Journal on Scientific Computing 1998; 19:302-318.
17. Oosterlee CW, Washio T. An evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed problems. SIAM Journal on Scientific Computing 1998; 19:87-110.
18. Dembo RS, Eisenstat SC, Steihaug T. Inexact Newton methods. SIAM Journal on Numerical Analysis 1982; 19:400-408.
19. Elman HC, Silvester DJ, Wathen AJ. Performance and analysis of saddle point preconditioners for the discrete steady state Navier-Stokes equations. Numerical Mathematics 2002; 90:665-688.