Efficient Cell-Vertex Multigrid Scheme for the Three-Dimensional Navier-Stokes Equations.

Abstract

A cell-vertex scheme for the 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 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 high-aspect-ratio cells, are discussed. Emphasis is placed on the analysis of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios.