Abstract:
The present paper investigates the high-order spectral finite volume 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 2-dimensional Euler spectral finite volume solver. The limiter formulation and geometry interpreter for high-order mesh generation are new contributions for the spectral finite volume method. Literature test cases are evaluated to assess the interaction of curved mesh, limiter and spatial reconstruction features of the spectral finite volume 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 spectral finite volume results are compared with those from different numerical methods.
KEYWORDS:
Spectral volume method; Compressible flows; High-order reconstruction; Unstructured grids
