Assessment of Preconditioning Methods for Multidimensional Aerodynamics

Abstract

We consider the steady equations for a compressible fluid. For low speed flow the system is stiff since the ratio of the convective speed of sound is very small. To overcome this difficulty we alter the time dependency of the equations while retaining the same steady state operator. In order to achieve high numerical resolution we also alter the artificial dissipation of the numerical scheme. The definition of preconditioners and artificial dissipation terms can be formulated conveniently by using other sets of dependent variables rather than the conservative variables. The effects of different preconditioners, artificial dissipation and grid density onaccuracy and convergence to the steady state of the numerical solutions are presented in detail. The numerical results obtained for inviscid and viscous 2D and 3D flows over external aerodynamic bodies indicate that efficient multigrid computations of flows with very low Mach numbers are now possible (see also 3).