On Chorin’s projection method for the incompressible Navier-Stokes equations. (English) Zbl 0769.76053

Rannacher, Rolf

The Navier-Stokes equations II - theory and numerical methods, Proc. Conf., Oberwolfach/Ger. 1991, Lect. Notes Math. 1530, 167-183 (1992).

[For the entire collection see Zbl 0759.00010.]
Pseudo-compressibility methods are frequently used in computational fluid dynamics in order to cope with the algebraic difficulties caused by the incompressibility constraint. A popular example is the pressure stabilization (Petrov-Galerkin) method which can be applied to the stationary as well as to the nonstationary Navier-Stokes problem. Also the classical projection method of A. J. Chorin can be interpreted as a variant of this method. This observation sheds some new light on the approximation properties of the projection method, particularly for the pressure.

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
76D05	Navier-Stokes equations for incompressible viscous fluids
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q30	Navier-Stokes equations

Keywords:

pseudo-compressibility methods; pressure stabilization method; incompressibility constraint

Citations:

Zbl 0759.00010