An Unstructured Grid Implementation of High-Order Spectral Finite Volume Schemes

The present work implements the spectral finite volume scheme in a cell centered finite volume context for unstructured meshes. The 2-D Euler equations are considered to rep-resent the flows of interest. The spatial discretization scheme is developed to achieve high resolution and computational efficiency for flow problems governed by hyperbolic conser-vation laws, including flow discontinuities. Such discontinuities are mainly shock waves in the aerodynamic studies of interest in the present paper. The entire reconstruction pro-cess is described in detail for the 2nd to 4th order schemes. Roe’s flux difference splitting method is used as the numerical Riemann solver. Several applications are performed in order to assess the method capability compared to data available in the literature. The results obtained with the present method are also compared to those of essentially non-oscillatory and weighted essentially non-oscillatory high-order schemes. There is a good agreement with the comparison data and efficiency improvements have been observed