On the penalty-projection method for the Navier-Stokes equations with the MAC mesh

Journal of Computational and Applied Mathematics

Volumn 226, Issue 2, 2009, Pages 228-245

  Fevriere C ^a   Laminie, J ^a   Poullet, P ^a   Angot, Ph ^b  

^a UNIVERSITÉ DES ANTILLES ET DE LA GUYANE   (France)

^b AIX MARSEILLE UNIVERSITY   (France)

Author keywords

Incompressible flows; MAC scheme; Navier Stokes equations; Penalty projection method; Projection methods

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; FLUID DYNAMICS; INCOMPRESSIBLE FLOW; SUBMARINE PIPELINES; VISCOUS FLOW;

BACKWARD DIFFERENCE FORMULAS; DIRICHLET BOUNDARY CONDITIONS; ENERGY METHODS; INCOMPRESSIBLE FLOWS; MAC SCHEME; NONLINEAR TERMS; OPEN BOUNDARY CONDITIONS; PENALTY-PROJECTION METHOD; PROJECTION METHODS; RICHARDSON EXTRAPOLATIONS; SECOND ORDERS; SPATIAL DISCRETIZATION; TIME DEPENDENTS;

NAVIER STOKES EQUATIONS;

EID: 60349089084     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.08.014     Document Type: Article

References (29)

1. Ph. Angot, M. Jobelin, J.-C. Latché, Error analysis of the penalty-projection method for the time-dependent Stokes equations, SIAM J. of Numer. Anal. 2008 (in press)
2. Chorin A.J. Numerical solution of the Navier-Stokes equations. Math. Comp. 22 (1968) 745-762
3. Févrière C., Angot Ph., and Poullet P. A penalty-projection method using staggered grids for incompressible flows. In: Lirkov I., Margenov S., and Wasniewski J. (Eds). Lecture Notes in Computer Science vol. 4818 (2008), Springer-Verlag, Berlin, Heidelberg 192-200
4. Fortin M., and Glowinski R. Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary Value Problems (1983), North-Holland
5. Guermond J.L. A result of second-order convergence in time for the approximation of Navier-Stokes equations using an incremental projection technique. M2AN Math. Modelling Numer. Anal. 33 1 (1999) 169-189
6. Guermond J.L., Minev P., and Shen J. Error analysis of pressure-correction schemes for the time-dependent Stokes equations with open boundary conditions. SIAM J. Numer. Anal. 43 1 (2005) 239-258
7. Guermond J.L., Minev P., and Shen J. An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng. 195 (2006) 6011-6045
8. Rannacher R. On Chorin's Projection Method for Incompressible Navier-Stokes Equations. Lecture Notes in Mathematics vol. 1530 (1992), Springer, Berlin 167-183
9. Prohl A. Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations (1997), B.G. Teubner, Stuttgart
10. Badia S., and Codina R. Convergence analysis of the FEM approximation of the first order projection method for incompressible flows with and without the inf-sup condition. Numer. Math. 107 4 (2007) 533-557
11. Guermond J.L., and Quartapelle L. An the approximation of the unsteady Navier-Stokes equations by finite element projection methods. Numer. Math. 80 (1998) 207-238
12. Guermond J.L., and Shen J. On the error estimates for the rotational pressure-correction projection methods. Math. Comp. 73 248 (2004) 1719-1737
13. Harlow F., and Welch J. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surfaces. J. Eur. Phys. Fluids 8 (1965) 2181-2189
14. Heywood J.G., and Rannacher R. Finite element approximation of the nonstationary Navier-Stokes problem. I. Regularity of solutions and second order error estimates for spatial discretization. SIAM J. Numer. Anal. 19 (1982) 275-311
15. Jobelin M., Piar B., Angot Ph., and Latché J.-C. Une méthode de pénalité-projection pour les écoulements dilatables. European J. Comput. Mech. 17 4 (2008) 453-480
16. Jobelin M., Lapuerta C., Latché J.-C., Angot Ph., and Piar B. A finite element penalty-projection method for incompressible flows. J. Comput. Phys. 217 2 (2006) 502-518
17. Peyret R., and Taylor T.D. Computational Methods for Fluid Flow (1983), Springer-Verlag
18. Poullet P. Staggered Incremental Unknowns for solving Stokes and generalized Stokes problems. Appl. Numer. Math. 35 1 (2000) 23-41
19. A. Quarteroni, A. Valli, Numerical Approximation of Partial Differential Equations, Springer Series in Computational Mathematics, vol. 23, Springer-Verlag
20. Shen J. On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations. Numer. Math. 62 (1992) 49-73
21. Shen J. Remarks on the pressure error estimates for the projection methods. Numer. Math. 67 (1994) 513-520
22. Shen J. On error estimates of the penalty method for unsteady Navier-Stokes equations. SIAM J. Numer. Anal. 32 2 (1995) 386-403
23. Shen J. On error estimates of projection methods for Navier-Stokes equations: Second-order schemes. Math. Comp. 65 215 (1996) 1039-1065
24. Temam R. Sur l'approximation de la solution des équations de Navier-Stokes par la méthode à pas fractionnaires (II). Arch. Ration. Mech. Anal. 33 (1969) 377-385
25. Temam R. Navier-Stokes Equations (2001), AMS Chelsea Publishing
26. Timmermans L., Minev P., and Van De Vosse F. An approximate projection scheme for incompressible flow using spectral elements. Int. J. Numer. Methods Fluids 22 (1996) 673-688
27. Van Kan J. A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Stat. Comput. 7 3 (1986) 870-891
28. Y. Saad, Preconditioning techniques for highly indefinite, the 9th IMACS International Symposium on Iterative Methods in Scientific Computing, March 17-20, 2008, Lille
29. Saad Y. Iterative Methods for Sparse Linear Systems (1996), PWS Publishing Company, Boston, MA