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.
Highlights
High-order numerical schemes represent the natural extension of current Computational Fluid Dynamics (CFD) methods, which were developed over the past 30 years for aerospace simulations
The results presented here attempt to validate the implementation of the data structure, temporal integration, numerical convergence stability and resolution of the spectral finite volume (SFV) method
The geometric coefficients for the weighted ENO (WENO) reconstructions are computed in a pre-processing step and kept in memory during the computation
Summary
High-order numerical schemes represent the natural extension of current Computational Fluid Dynamics (CFD) methods, which were developed over the past 30 years for aerospace simulations. The current generation methods are mostly 2nd-order accurate in space and have achieved a level of maturity and robustness desirable for everyday use in aeronautical engineering scenarios. Several complementary methods were developed for time integration, convergence acceleration, shock capturing and geometry flexibility. There are many problems that cannot be fully simulated using low-order methods, such as vortex dominated flows. This observation has motivated the CFD community to consider high-order methods for unstructured meshes.
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