A Multigrid Semi-Implicit Line Method for Viscous Incompressible and Low-Mach-Number Flows on High Aspect Ratio Grids

Jan Vierendeels, Kris Riemslagh, and Erik Dick
Department of Mechanical and Thermal Engineering
Universiteit Gent, Belgium

Abstract

Discretization of viscous incompressible and viscous low-Mach-number flows often leads to a system of equations, which is very difficult to solve. There are two reasons. First, the use of high aspect ratio grids results in a very numerically anisotropic behaviour of the diffusive and acoustic terms and second, in low-Mach-number flow, the ratio of the convective and acoustic eigenvalues of the inviscid system becomes very high.

We implemented an AUSM based discretization method, using an explicit third-order discretization for the convective part, a line-implicit central discretization for the acoustic part and for the diffusive part. The lines are chosen in the direction of the gridpoints with shortest connection. The preconditioned semi-implicit line method is used in multistage form because of the explicit third-order discretization of the convective part. Multigrid is used as acceleration technique.

It is shown that the convergence is very good, independent of grid aspect ratio and Mach number.