The Effect of Discretization Order for Governing Equations on the Solution Accuracy

Abstract

To obtain high order accurate numerical solutions with the finite volume method, the Euler or the Navier-Stokes equations are discretized with the second order accuracy and cell-face numerical fluxes are then calculated by high order accurate shock-capturing schemes such as ENO/WENO. In this approach, numerical dissipations are added due to built-in second order discretization errors. In this work, a discretization method with fourth order spatial accuracy is proposed. We investigate the effect of discretization order and numerical flux order on the solution accuracy using the third order MUSCL and fifth order WENO schemes for cell-face numerical fluxes.