Preconditioning Methods for Low-Speed Flows

We consider the steady-state equations for a compressible fluid. For low-speed flow, the system is stiff because the ratio of the convective speed to the speed of sound is quite small. To overcome this difficulty, we alter the time evolution of the equations but retain the same steady-state analytic equations. To achieve high numerical resolution, we also alter the artifi-cial viscosity of the numerical scheme, which is implemented conveniently by using other sets of variables in addition to the conservative variables. We investigate the effect of the artifi-cial dissipation within this preconditioned system. We consider both the nonconservative and conservative formulations for artificial viscosity and examine their effect on the accuracy and convergence of the numerical solutions. The numerical results for viscous three-dimensional wing flows and two-dimensional multi-element airfoil flows indicate that efficient multigrid computa-tions of flows with arbitrarily low Mach numbers are now possible with only minor modifications to existing compressible Navier-Stokes codes. The conservative formulation for artificial viscos-ity, coupled with the preconditioning, offers a viable computational fluid dynamics (CFD) too