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

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... llatory (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.