A multigrid semi-implicit line-method for viscous incompressible and low-Mach-number flows on high aspect ratio grids

Discretization of viscous incompressible and viscous low-Mach-number flows often leads to a system of equations, which is very difficult to solve. The re an two reasons. First, the use of high aspect ratio grids results in a v ery numerically anisotropic behaviour of the diffusive and acoustic terms a nd second, in low-Machnumber flow, the ratio of the convective and acoustic eigenvalues of the inviscid system becomes very high. We implemented an AU SM based discretization method, using an explicit third-order discretizatio n for the convective part and a line-implicit central discretization for th e acoustic part and for the diffusive part. The lines are chosen in the dir ection of the grid points with shortest connection. The preconditioned semi -implicit line method is used in multistage form because of the explicit th ird-order discretization of the convective part. Multigrid is used as an ac celeration technique. It is shown that the convergence is very good, indepe ndent of grid aspect ratio and Mach number. (C) 1999 Academic Press.