Comparison of finite volume high-order schemes for the two-dimensional Euler equations

Abstract

The present paper describes the use of various high-order schemes in a finite volume formulation for use on structured grids. In particular, WENO and compact upwind schemes as well as central and upwind schemes are investigated. Their efficiency and accuracy are compared to the well-established second- and third-order MUSCL family of schemes. The different schemes are analyzed and tested numerically using canonical flow problems in the context of the two-dimensional Euler equations. Results are shown for the two-dimensional advection of a density pulse to quantify the dissipation and dispersion properties of the schemes. To investigate the non-oscillatory nature of the schemes and the resolution of discontinuities the Riemann problem is analyzed. The simulations are performed on uniform as well as non-uniform meshes.