Efficient cell-centered multigrid scheme for the three-dimensional Navier-Stokes equations

A cell-centered scheme for three-dimensional Navier-Stokes equations, which is based on central-difference approximations and Runge-Kutta time stepping, is described. By using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, good convergence rates are obtained for two- and three-dimensional flows. The emphases are on the implicit smoothing and artificial dissipative terms with locally variable coefficients which depend on cell aspect ratios. The computational results for two-dimensional subsonic airfoil flows and three-dimensional transonic C-D nozzle flows are essentially coincident with other experimental and calculated results.