Enhanced numerical inviscid and viscous fluxes for cell centered finite volume schemes

Abstract

Abstract The most attractive features of cell centered finite volume schemes seem to be the easy introduction of the solid body boundary condition and the implementation of characteristic based methods for evaluating the convective fluxes at the cell faces of the finite volumes. For the viscous parts of the fluxes, however, cell centered finite volume schemes are not as well-suited as cell vertex based discretizations since, in a general grid, cell centered schemes usually are not linear flow preserving concerning the viscous terms. That means that the viscous stress tensor and the heat flux vector may vary spuriously in a flow field with linear velocity and/or temperature distribution. This paper describes several enhancements of the flux formulations for cell centered finite volume schemes concerning convective as well as viscous fluxes: Convective fluxes • — Non-iterative solution of the cell face Riemann problem. • — Rigorous exploitation of the homogeneous property for high accuracy. • — Differentiable high-order positive flux limiting. • — Blending with flux vector splitting for strong shock capturing. Viscous fluxes • — Correct local geometry mapping for linear flow preservation. • — Implementation of stresses and heat fluxes by Stokes' integral for convenient boundary condition implementation.