Further Development and Application of High-Order Spectral Volume Methods for Compressible Flows

Abstract

The present work investigates the high-order spectral finite volume (SFV) method with emphasis on applicability aspects for compressible flows. The intent is to improve the understanding and implementation of numerical techniques related to high-order unstructured grid schemes. In that regard, a hierarchical moment limiter and high-order mesh capability are developed for a two-dimensional Euler SFV solver. The limiter formulation and geometry interpreter for high-order mesh creation are new contributions for the SFV method. Literature test cases are evaluated to assess the interaction of curved mesh, limiter and spatial reconstruction features of the SFV scheme. An order of accuracy study is presented along with steady and unsteady problems with strong shock waves and other discontinuities typical of compressible flows. Moreover, second, third and fourth-order spatial resolution analyses are explored and the SFV results are compared with results from different numerical methods.