Efficient Computation of Transonic Viscous Flows with a Multigrid Scheme.

Abstract

A cell-vertex scheme for the three-dimensional Navier-Stokes equations, based on central-difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing with locally varying coefficients, a multigrid method and carefully controlled dissipative terms, very good convergence rates are obtained for two- and three-dimensional flows. Details of the acceleration techniques which are important for convergence on meshes with aspect-ratio cells, are discussed. Emphasis is put on the analysis of the implicit smoothing of the explicit residuals with coefficients which depend on cell aspect ratios.