Multigrid methods for the stokes system

Computing in Science and Engineering

Volumn 8, Issue 6, 2006, Pages 34-43

  Oosterlee, Cornelis W ^a   Lorenz, Francisco José Gaspar ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

MULTIGRID METHODS; NAVIER-STOKES EQUATIONS; PROBLEM FORMULATION; STOKES SYSTEMS;

COMPUTER SCIENCE; DISCRETE TIME CONTROL SYSTEMS; LINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SYSTEM STABILITY;

DISTRIBUTED COMPUTER SYSTEMS;

EID: 33750829753     PISSN: 15219615     EISSN: None     Source Type: Journal    
DOI: 10.1109/MCSE.2006.115     Document Type: Review

References (22)

1. U. Trottenberg, C.W. Oosterlee, and A. Schüller, MultigridAcademic Press, 2001.
2. J.W. Ruge and K. Stüben, "Algebraic Multigrid (AMG)," Multigrid Methods, Frontiers in Applied Mathematics, S.F. McCormick, ed., SIAM Press, 1987, pp. 73-130.
3. A. Brandt, "Multi-Level Adaptive Solutions to Boundary-Value Problems, Mathematics of Computation, vol. 31, 1977, pp. 333-390.
4. A. Brandt and N. Dinar, "Multigrid Solutions to Elliptic Flow Problems," Numerical Methods for Partial Differential Equations, S. Parter, ed., Academic Press, 1979, pp. 53-147.
5. G. Wittum, "Multi-Grid Methods for Stokes and Navier-Stokes Equations with Transforming Smoothers: Algorithms and Numerical Results," Numerische Mathematik, vol. 54, 1989, pp. 543-563.
6. S.P. Vanka, "Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables," J. Computational Physics, vol. 65, 1986, pp. 138-158.
7. W. Rodi, S. Majumdar, and B. Schönung, "Finite Volume Methods for Two-Dimensional Incompressible Flow Problems with Complex Boundaries," Computational Methods in Applied Mechanics and Eng., vol. 75, 1989, pp. 369-392.
8. P. Wesseling, Principles of Computational Fluid Dynamics, Springer, 2001.
9. F.H. Harlow and J.E. Welch, "Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with a Free Surface," Physics of Fluids, vol. 8, 1965, pp. 2182-2189.
10. P. Wesseling, An Introduction to Multigrid Methods, John Wiley & Sons, 1992.
11. P. Wesseling and C.W. Oosterlee, "Geometric Multigrid with Applications to Computational Fluid Dynamics," J. Computational and Applied Mathematics, vol. 128, 2001, pp. 311-334.
12. A. Niestegge and K. Witsch, "Analysis of a Multigrid Stokes Solver," Applied Mathematics and Computation, vol. 35, 1990, pp. 291-303.
13. S. Sivaloganathan, "The Use of Local Mode Analysis in the Design and Comparison of Multigrid Methods," Computer Physics Comm., vol. 65, 1991, pp. 246-252.
14. P. Sockol, "Multigrid Solution of the Navier-Stokes Equations on Highly Stretched Grids," Int'l. J. Numerical Methods in Fluids, vol. 17, 1993, pp. 543-566.
15. M.F. Paisley and N.M. Bhatti, "Comparison of Multigrid Methods for Neutral and Stably Stratified Flows over Two-Dimensional Obstacles," J. Computational Physics, vol. 142, 1998, pp. 581-610.
16. A.J. Chorin, "A Numerical Method for Solving Incompressible Viscous Flow Problems," J. Computational Physics, vol. 2, 1967, pp. 12-26.
17. J. Shen, "On Error Estimates of Projection Methods for the Navier-Stokes Equations: Second-Order Schemes," Mathematics of Computation, vol. 65, 1996, pp. 1039-1065.
18. J. van Kan, "A Second-Order Accurate Pressure-Correction Scheme for Viscous Incompressible Flow," SIAM J. Scientific Computing, vol. 7, 1986, pp. 870-891.
19. J. Linden, B. Steckel, and K. Stüben, "Parallel Multigrid Solution of the Navier-Stokes Equations on General 2D-Domains," Parallel Computing, vol. 7, 1988, pp. 461-475.
20. J.H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002.
21. H. Elman, D. Silvester, and A. Wathen, Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics, Oxford Science, 2005.
22. A. Schüller, "A Multigrid Algorithm for the Incompressible Navier-Stokes Equations," Numerical Treatment of Navier-Stokes Equations, Notes on Numerical Fluid Mechanics, W. Hackbusch and R. Rannacher, eds., Vieweg, 1990, pp. 124-133.