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

  • Authors:

  • Yu-Xin Ren;Yutao Sun

  • Affiliations:

  • Department of Engineering Mechanics, Tsinghua University, Qinghuayuan, Beijing, PR China;Department of Engineering Mechanics, Tsinghua University, Qinghuayuan, Beijing, PR China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

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.