A comparative study of discontinuous high order methods for compressible flows

Abstract

A comparative study of three numerical formulations for discontinuous high-order reconstruction on unstructured grids is performed. TheWeighted Essentially Non-Oscillatory (WENO), the Spectral Finite Volume (SFV) and the Spectral Difference (SD) methods are considered for the spatial discretization of the 2-D Euler equations. The study compares, in particular, results for linear, quadratic and cubic reconstructions. The test cases include problems with strong shock waves and other discontinuities which provide a comparative assessment of the resolution capability of the tested schemes. This work explores the high-order method capabilities to solve literature test cases and it is expected that such results provide valuable guidelines for future developments regarding high-order methods for aerospace applications