A multi-dimensional upwind scheme for solving Euler and Navier–Stokes equations

This paper presents a multi-dimensional upwind finite volume scheme for solving the gasdynamic Euler and Navier–Stokes equations. In evaluating the inviscid numerical fluxes, the full governing equations are solved on every cell interface to account for the multi-dimensional effects. To make the scheme efficient, the governing equations are solved on every cell interface using an operator splitting method: in the first step, the contribution of inviscid terms is modeled by solving the linearized Euler equations in characteristic form; in the second step, the contribution of viscous terms are included by a simple correction procedure. The resulted scheme is efficient and easy to be applied on general control volumes. Several numerical test cases are presented to verify the proposed scheme.