A New Discretization Method Of Governing Equations For High Order Accuracy

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 calculated by high order accurate shock-capturing schemes such as ENO/WENO. In that 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 numerical fluxes.