OPTIMAL MULTISTAGE SCHEMES FOR EULER EQUATIONS WITH RESIDUAL SMOOTHING

A numerical technique, composed of the Van Leer-Tai-Powell optimizatio n and a modified procedure, is applied to design multistage schemes th at give optimal damping of high frequencies for given upwind-biased sp atial differencing with implicit and explicit residual smoothing. The analysis is done for a scalar convection equation in one space dimensi on. The object of this technique is to make the schemes suited for mul tigrid acceleration. The optimal multistage schemes and their damping properties are presented in this paper. By keeping the multistage coef ficients from the one-dimensional analysis and simply redefining the C ourant number, the schemes can be applied to multidimensional problems . A fast Euler code is used to evaluate the suitability of the schemes for multidimensional multigrid computations. Numerical results show t hat the modified schemes effectively enhance the convergence performan ce on both single and multiple grids.