Pressure correction algebraic splitting methods for the incompressible Navier-Stokes equations

SIAM Journal on Numerical Analysis

Volumn 43, Issue 1, 2005, Pages 174-194

  Saleri, F ^a   Veneziani, A ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Fractional steps schemes; Incompressible Navier Stokes equations

Indexed keywords

COMPRESSIBILITY; INCOMPRESSIBLE FLOW; INTRANETS; NAVIER STOKES EQUATIONS;

FRACTIONAL STEPS SCHEMES; INCOMPRESSIBLE NAVIER-STOKES EQUATIONS;

ALGEBRA;

EID: 20044381802     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903435429     Document Type: Article

References (27)

1. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer Ser., Comput. Math. 15, Springer-Verlag, New York, 1991.
2. T. F. CHAN AND W. L. WAN, Analysis of projection methods for solving linear systems with multiple right-hand sides, SIAM J. Sci. Comput., 18 (1997), pp. 1698-1721.
3. A. CHORIN, Numerical solution of the Navier-Stokes equations, Math. Comp., 22 (1968), pp. 745-762.
4. G. COHEN, P. JOLY, J. E. ROBERTS, AND N. TORDJMAN, Higher order triangular finite elements with mass lumping for the wave equation, SIAM J. Numer. Anal., 38 (2001), pp. 2047-2078.
5. M. O. DEVILLE, P. F. FISCHER, AND E. H. MUND, High Order Methods for Incompressible Fluid Flow, Cambridge University Press, Cambridge, UK, 2002.
6. J. DONEA AND A. HUERTA, Finite Element Methods for Flow Problems, John Wiley and Sons, New York, 2003.
7. H. C. ELMAN, Preconditioning for the steady-state Navier-Stokes equations with low viscosity, SIAM J. Sci. Comput., 20 (1999), pp. 1299-1316.
8. P. FISCHER, Projection techniques for iterative solution of ax=b with successive right-hand sides, Comput. Methods Appl. Mech. Eng., 163 (1998), pp. 193-204.
9. A. GAUTHIER, F. SALERI, AND A. VENEZIANI, A fast preconditioner for the incompressible Navier-Stokes equations, Comput. Vis. Sci., 6 (2004), pp. 105-112.
10. J. GUERMOND, Un resultat de convergence d'ordre deux en temps pour l'approximation des equations de Navier-Stokes par une technique de projection incrementale, M2AN Math. Model. Numer. Anal., 33 (1999), pp. 169-189.
11. J. GUERMOND, P. MINEV, AND J. SHEN, Error Analysis of Pressure-Correction Schemes for the Navier-Stokes Equations with Open Boundary Conditions, TICAM report 03-08, Institute for Computational Engineering and Science, Austin, TX, 2003.
12. J. GUERMOND AND J. SHEN, A new class of truly consistent splitting schemes for incompressible flows, J. Comput. Phys., 192 (2003), pp. 262-276.
13. J. L. GUERMOND AND J. SHEN, Velocity-correction projection methods for incompressible flows, SIAM J. Numer. Anal., 41 (2003), pp. 112-134.
14. J.-L. GUERMOND AND L. QUARTAPELLE, On the approximation of the unsteady Navier-Stokes equations by finite element projection methods, Numer. Math., 80 (1998), pp. 207-238.
15. M. HENRIKSEN AND J. HOLMEN, Algebraic splitting for incompressible Navier-Stokes equations, J. Comput. Phys., 175 (2002), pp. 438-453.
16. J. VAN KAN, A second-order accurate pressure-correction scheme for viscous incompressible flow, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 870-891.
17. J. KIM AND P. MOIN, Application of a fractional step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59 (1985), pp. 308-323.
18. G. M. KOBELKOW AND M. OLSHANSKII, Effective preconditioning of Uzawa type schemes for a generalized Stokes problem, Numer. Math., 86 (2000), pp. 443-470.
19. P. MATSTOMS, Sparse QR Factorization with Application to Linear Least Squares Problems, Ph.D. thesis, Linköping University, Sweden, 1994.
20. B. PEROT, An analysis of the fractional step method, J. Comput. Phys., 108 (1993), pp. 51-58.
21. A. PROHL, Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations, Springer-Verlag, 1997.
22. A. QUARTERONI, F. SALERI, AND A. VENEZIANI, Analysis of the Yosida method for the incompressible Navier-Stokes equations, J. Math. Pures Appl. (9), 78 (1999), pp. 473-503.
23. A. QUARTERONI, F. SALERI, AND A. VENEZIANI, Factorization methods for the numerical approximation of Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 188 (2000), pp. 505-526.
24. A. QUARTERONI AND A. VALLI, Numerical Approximation of Partial Differential Equations, Springer Ser. Comput. Math. 23, Springer-Verlag, Berlin, 1994.
25. J. SHEN, On error estimates of the projection methods for Navier-Stokes equations: Second order schemes, Math. Comp., 65 (1996), pp. 1039-1065.
26. L. TIMMERMANS, P. MINEV, AND F. V. DE VOSSE, An approximate projection scheme for incompressible flow using spectral methods, Internat. J. Numer. Methods Fluids, 22 (1996), pp. 673-688.
27. A. VENEZIANI, Block factorized preconditioners for high-order accurate in time approximation of the Navier-Stokes equations, Num. Methods Partial Differential Equations, 19 (2003), pp. 487-510.