An efficient implicit multigrid method is presented for the Navier-Stokes and k- turbulence equations. Freezing and limiting strategies are applied to improve the robustness and convergence of the multigrid method. In this work, the eddy viscosity and strongly nonlinear production terms of turbulence are frozen in the coarser grids by passing down the values without update of them. The turbulence equations together with the Navier-Stokes equations, however, are consecutively solved on the coarser grids in a loosely coupled fashion. A simple limit for k is also introduced to circumvent slow-down of convergence. Numerical results for the unseparated and separated transonic airfoil flows show that all computations converge well to nine order of magnitude of error without any robustness problem and the computing time is reduced to a factor of about 3 by the present multigrid method.
Computational technologies for Fluid/Thermal/Structural/Chemical Systems with Industrial Applications (2002 ASME Prssure Vessels and Piping Conference), v.448, no.1, pp.35 - 44