An iterative solver for the Oseen problem and numerical solution of incompressible Navier–Stokes equations

✍ Scribed by Maxim A. Olshanskii

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 136 KB
• Volume: 6
• Category: Article
• ISSN: 1070-5325
• DOI: 10.1002/(sici)1099-1506(199907/08)6:5<353::aid-nla169>3.0.co;2-j

✦ Synopsis

Incompressible unsteady Navier-Stokes equations in pressure -velocity variables are considered. By use of the implicit and semi-implicit schemes presented the resulting system of linear equations can be solved by a robust and efficient iterative method. This iterative solver is constructed for the system of linearized Navier-Stokes equations. The Schur complement technique is used. We present a new approach of building a non-symmetric preconditioner to solve a non-symmetric problem of convection-diffusion and saddle-point type. It is shown that handling the differential equations properly results in constructing efficient solvers for the corresponding finite linear algebra systems. The method has good performance for various ranges of viscosity and can be used both for 2D and 3D problems. The analysis of the method is still partly heuristic, however, the mathematically rigorous results are proved for certain cases. The proof is based on energy estimates and basic properties of the underlying partial differential equations. Numerical results are provided. Additionally, a multigrid method for the auxiliary convection-diffusion problem is briefly discussed.