A High Order Accurate Unstructured Spectral Finite Volume Implicit Algorithm for Inviscid Compressible Flows

Abstract. The purpose of this work is to develop a methodology that achieves high order spatial discretization for compressible aerodynamic flows based on the spectral finite volume method for hyperbolic conservation laws. 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 other words, high order methods can potentially achieve a higher level of accuracy than low order ones given the same computational resources. The spectral finite volume method was developed as an alternative to k-exact high order schemes, ENO/WENO and discontinuous Galerkin methods. Its main objective is to allow the implementation of a simpler and more efficient scheme, while still achieving high order spatial accuracy. The 2-D Euler equations are solved numerically in a finite volume, cell centered context on unstructured meshes. An implicit time march algorithm is employed to advance the solution to steady-state. The treatment of discontinuities is also discussed. Several applications are performed in order to assess the method capability, which is compared to data available in the literature and also compared to results from an weighted essentially non-oscillatory (WENO) scheme. The latter comparison data can also be used to assess the present method computational performance.