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.