Upwind scheme for solving the Euler equations on unstructured tetrahedral meshes

Abstract

An upwind scheme is presented for solving the three-dimensional Euler equations on unstructured tetrahedral meshes. Spatial discretization is accomplished by a cell-centered finite-volume formulation using flux-difference splitting. Higher-order differences are formed by a multidimensional linear reconstruction process. The solution gradients required for the higher-order differenes are computed by a novel approach that yields highly resolved solutions in regions of smooth flow while avoiding oscillations across shocks without explicitly applying a limiter. Solutions are advanced in time by a three-stage Runge-Kutta time-stepping scheme with convergence accelerated to steady state by local time stepping and implicit residual smoothing. Transonic solutions are presented for two meshes around the ONERA M6 wing and demonstrate substantial accuracy and insensitivity to mesh size.