No abstract

A comparative study of three numerical formulations for discontinuous high-order reconstruction on unstructured grids is performed. The Weighted 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.

Abstract. The purpose of this work is to compare two numerical formulations for unstructured grids that achieve high-order spatial discretization for compressible aerodynamic flows. High-order methods are necessary on the analysis of complex flows to reduce the number of mesh elements one would otherwise need if using traditional second-order schemes. In the present work, the 2-D Euler equations are solved numerically in a finite volume, cell centered context. The third-order Weighted Essentially Non-Oscillatory (WENO) and Spectral Finite Volume (SFV) methods are considered in this study for the spatial discretization of the governing equations. Time integration uses explicit, Runge-Kutta type schemes. Two literature test cases, one steady and one unsteady, are considered to assess the resolution capabilities and performance of the two spatial discretization methods. Both methods are suitable for the aerospace applications of interest. However, each method has characteristics that excel over the other scheme. The present results are valuable as a form of providing guidelines for future developments regarding high-order methods for unstructured meshes.