A Nonlinear Multigrid Method for the Three-Dimensional Incompressible Navier-Stokes Equations

Journal of Computational Physics

Volumn 146, Issue 1, 1998, Pages 301-321

  Drikakis, D ^a   Iliev, O P ^b   Vassileva, D P ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

Artificial compressibility; Multigrid; Navier Stokes equations; Upwind schemes

Indexed keywords

APPROXIMATION ALGORITHMS; COMPRESSIBILITY; NONLINEAR EQUATIONS; RUNGE KUTTA METHODS; VISCOUS FLOW;

ARTIFICIAL COMPRESSIBILITY; COARSE GRID; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; INCOMPRESSIBLE NAVIER STOKES EQUATIONS; MULTIGRID METHODS; MULTIGRIDS; NAVIER-STOKES EQUATION; NONLINEAR MULTIGRID; THREE-DIMENSIONAL NAVIER-STOKES EQUATIONS; UP-WIND SCHEME;

NAVIER STOKES EQUATIONS;

EID: 0000078356     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6067     Document Type: Article

References (32)

1. Fedorenko R. P. A relaxation method for solving elliptic difference equations. USSR Comput. Math. Phys. 1:1961;1092.
2. Bakhvalov N. S. On the convergence of a relaxation method with natural constraints on the elliptic operator. USSR Comput. Math. Phys. 6:1966;101.
3. Brandt A. A multilevel adaptive solutions of boundary value problems. Math. Comput. 31:1977;333.
4. Hackbusch W. Multi-Grid Methods and Applications. 1985.
5. Wesseling P. An Introduction to Multigrid Methods. 1991.
6. Cope W. K., Wang G., Vanka S. P. A staggered grid multilevel method for the simulation of fluid flow in 3-D complex geometries. AIAA Paper 94-0778. 1994.
7. Chorin A. J. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2:1967;12.
8. Farmer J., Martinelli L., Jameson A. A fast multigrid method for solving incompressible hydrodynamic problems with free surfaces. AIAA-93-0767. 1993.
9. Sheng Ch., Taylor L. K., Whitfield D. L. An efficient multigrid acceleration for solving the 3D incompressible Navier-Stokes equations in generalized curvilinear coordinates. AIAA-93-2335. 1994.
10. Sheng Ch., Taylor L. K., Whitfield D. L. AIAA J. 33:1995.
11. Jameson A. Solution of the Euler equations for two dimensional transonic flow by a multigrid method. Appl. Math. Comput. 13:1983;327.
12. Jameson A. Computational transonics. Comm. Pure Appl. Math. 41:1988;507.
13. A. Jameson, A vertex based multigrid algorithm for three-dimensional compressible flow calculations, ASME Symposium on Numerical Methods for Compressible Flows, Annaheim, December, 1986.
14. Liu F., Jameson A. Multigrid Navier-Stokes calculations for three-dimensional cascades. AIAA J. 31:1993;1785.
15. H. Kuerten, B. Geurts, Compressible turbulent flow simulation with a multigrid multiblock method, Proc. Copper Mountain Multigrid Conference, 1993, 305.
16. Lin F. B., Sotiropoulos F. Strongly-coupled multigrid method for 3D incompressible flows using near-wall turbulence closures. J. Fluids Engnrg. 119:1997;314.
17. Dailey L. D., Pletcher R. H. Evaluation of multigrid acceleration for preconditioned time-accurate Navier-Stokes algorithms. Comput. Fluids. 25:1996;791.
18. Lotstedt P. Improved convergence to the steady state of the Euler equations by enhanced wave propagation. J. Comput. Phys. 114:1994;34.
19. Steelant J., Dick E., Pattijn S. Analysis of robust multigrid methods for steady viscous low Mach number flows. J. Comput. Phys. 136:1997;603.
20. Drikakis D., Govatsos P., Papantonis D. A characteristic based method for incompressible flows. Int. J. Num. Meth. Fluids. 19:1994;667.
21. Drikakis D. A parallel multiblock characteristics-based method for three-dimensional incompressible flows. Adv. Eng. Software. 26:1996;111.
22. Radespiel R., Swanson R. C. Progress with multigrid schemes for hypersonic flow problems. J. Comput. Phys. 116:1995;103.
23. Vassilevski P. S. Preconditioning nonsymmetric and indefinite finite element matrices. J. Numer. Lin. Alg. Appl. 1:1992;59.
24. Xu J. New class of iterative methods for non-self adjoint or indefinite problems. SIAM J. Numer. Anal. 29:1992;303.
25. Xu J. A novel two-grid method for semilinear elliptic equations. SIAM J. Sci. Comput. 15:1994;231.
26. Ålund A., Lotstedt P., Silen M. Parallel single and multiple grid solution of industrial compressible flow problems. SAAB Military Aircraft Report. 15.11.1996.
27. O. Axelsson, M. Neytcheva, Scalable parallel algorithms in CFD computations, Computational Fluid Dynamics Review, 1995, 837.
28. Axelsson O., Neytcheva M. Some basic facts for efficient massively parallel computation. CWI Quart. 9:1996;9.
29. Beavers G. S., Sparrow E. M., Magnusson R. A. Experiments on hydrodynamically developing flow in rectangular ducts. Int. J. Heat Mass Transfer. 13:1970;689.
30. Goldstein R. J., Kreid D. K. Measurement of laminar flow development in a square duct using a laser-doppler flowmeter. J. Appl. Mech. Ser. E. 89:1967;813.
31. de Zeeuw P. M. Acceleration of Iterative Methods by Coarse Grid Corrections. 1996.
32. Humphrey A. C., Taylor A. M. K., Whitelaw J . H. Laminar flow in a square duct of strong curvature. J. Fluid Mech. 83:1977;509.