SOLUTIONS OF HYPERSONIC VISCOUS FLOWS WITH TOTAL VARIATION DIMINISHING MULTIGRID TECHNIQUES

In the present paper a multigrid technique based on the Full Approxima tion Storage Full Multigrid method with ''V-cycle'' strategy and direc tional grid transfer operators has been developed for hypersonic visco us hows. A truly two-dimensional stability analysis of the strategy ha s been developed to assess the damping properties and the influence of grid transfer operators. The full Navier-Stokes equations are solved by a finite volume approach based on a total variation diminishing dis cretization and explicit Runge-Kutta algorithm. The technique has been applied to compute simple and complex hypersonic hows, showing that f aster convergence is achieved by means of upwind prolongation operator s. However, for supersonic hows the technique shows no advantage over the standard approach.