A Cell-Vertex Upwind Scheme with Flux Balance Splitting for the Euler and Navier-Stokes Equations on Structured Meshes

Abstract

A cell-vertex upwind scheme for the solution of the Euler and Navier-Stokes equations on structured meshes is presented. At steady state, the cell-vertex Flux Balance Splitting scheme yields second order accurate solutions for inviscid and viscous flows. Computational results of inviscid flows are shown for two- and three-dimensional flows. Viscous flow is computed for the transonic flow around an airfoil. The cell-vertex upwind scheme yields accurate solutions on relatively coarse meshes, and the convergence rates are comparable to those of central differencing schemes. Using the cell-vertex upwind scheme on coarse meshes while retaining the same quality of the solution, a substantial reduction of computation time and memory requirements can be achieved compared to standard central differencing schemes.