On a new pseudocompressibility method for the incompressible Navier-Stokes equations

Applied Numerical Mathematics

Volumn 21, Issue 1, 1996, Pages 71-90

  Shen, Jie ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Artificial compressibility; Navier Stokes equations; Perturbation; Pressure stabilization; Projection method; Pseudocompressibility

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF STATE OF SOLIDS; ERROR ANALYSIS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES;

ARTIFICIAL COMPRESSIBILITY; PRESSURE STABILIZATION; PROJECTION METHOD; PSEUDOCOMPRESSIBILITY;

NAVIER STOKES EQUATIONS;

EID: 0030149512     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/0168-9274(95)00132-8     Document Type: Article

References (31)

1. S. Agmon, Lectures on Elliptic Boundary Value Problems (Elsevier, New York, 1965).
2. F. Brezzi and J. Douglas, Stabilized mixed methods for the Stokes problem, Numer. Math. 53 (1988) 225-235.
3. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer, New York, 1991).
4. F. Brezzi and J. Pitkaranta, On the stabilization of finite element approximation of the Stokes problem, in: W. Hackbusch, ed., Efficient Solutions of Elliptic Systems, Notes on Numerical Fluid Mechanics 10 (Vieweg, Braunschweig, 1984) 11-19.
5. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods on Fluid Dynamics (Springer, Berlin, 1987).
6. A.J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comp. 22 (1968) 745-762.
7. A.J. Chorin, On the convergence of discrete approximations to the Navier-Stokes equations, Math. Comp. 23 (1969) 341-353.
8. W. E and J.G. Liu, Projection method I: Convergence and numerical boundary layers, SIAM J. Numer. Anal. 32 (1995) 1017-1057.
9. V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations (Springer, Berlin, 1986).
10. J.G. Heywood and R. Rannacher, 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.
11. T.J.R. Hughes, L.P. Franca and M. Balestra, A new finite element formulation for computational fluid mechanics: V. Circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal order interpolation, Comput. Methods Appl. Mech. Engrg. 59 (1986) 85-99.
12. T.J.R. Hughes, W.T. Liu and A.J. Brooks, Finite element analysis of incompressible viscous flows by the penalty function formulation, J. Comput. Phys. 30 (1979) 1-60.
13. J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys. 59 (1985) 308-323.
14. S. Klainerman and A. Majda, Compressible and incompressible fluids, Comm. Pure Appl. Math. 35 (1982) 629-651.
15. H.O. Kreiss, J. Lorenz and J.M. Naughton, Convergence of the solutions of the compressible to the solution of the incompressible Navier-Stokes equations, Adv. in Appl. Math. (1991).
16. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Nonlinéaires (Dunod, Paris, 1969).
17. 1 piecewise polynomials of degree n ≥ 5, Math. Comp. 29 (1975) 736-740.
18. R. Rannacher, On Chorin's projection method for the incompressible Navier-Stokes equations, in: The Navier-Stokes Equations II. Theory and Numerical Methods, Lecture Notes in Mathematics 1530 (1991) 167-183.
19. R. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, Math. Model. Numer. Anal. 19 (1985) 111-143.
20. J. Shen, On error estimates of the projection methods for the Navier-Stokes equations: first-order schemes, SIAM J. Numer. Anal. 29 (1992) 57-77.
21. J. Shen, On pressure stabilization method and projection method for unsteady Navier-Stokes equations, in: R. Vichnevetsky, D. Knight and G. Richter, eds., Advances in Computer Methods for Partial Differential Equations (IMACS, 1992) 658-662.
22. J. Shen, On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations, Numer. Math. 62 (1992) 49-73.
23. J. Shen, A remark on the projection-3 method, Internat. J. Numer. Methods Fluids 16 (1993) 249-253.
24. J. Shen, On error estimates of the penalty method for the unsteady Navier-Stokes equations, SIAM J. Numer. Anal. 32 (2) (1995).
25. J. Shen, On error estimates of the projection method for the Navier-Stokes equations: second order schemes, Math. Comp. 65 (1996).
26. R. Temam, Une méthode d'approximation des solutions des équations de Navier-Stokes, Bull. Soc. Math. France 98 (1968) 115-152.
27. R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires II, Arch. Rational Mech. Anal. 33 (1969) 377-385.
28. R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires I, Arch. Rational Mech. Anal. 32 (1969) 135-153.
29. R. Temam, Navier-Stokes equations and nonlinear functional analysis, in: CBMS-NSF Regional Conference Series in Applied Mathematics 41 (SIAM, Philadelphia, 1983).
30. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis (North-Holland, Amsterdam, 1984).
31. J. van Kan, A second-order accurate pressure-correction scheme for viscous incompressible flow, SIAM J. Sci. Statist. Comput. 7 (1986) 870-891.