2020/11/06 by Johannes Markert, Gregor J. Gassner, Markert, Johannes +3
Engineering · #65Z05 #Advanced Numerical Methods in Computational Mathematics #Astrophysics of Galaxies (astro-ph.GA) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2011.03338
openalex publication_date 2020/11/06 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper, a new strategy for a sub-element based shock capturing for\ndiscontinuous Galerkin (DG) approximations is presented. The idea is to\ninterpret a DG element as a collection of data and construct a hierarchy of low\nto high order discretizations on this set of data, including a first order\nfinite volume scheme up to the full order DG scheme. The different DG\ndiscretizations are then blended according to sub-element troubled cell\nindicators, resulting in a final discretization that adaptively blends from low\nto high order within a single DG element. The goal is to retain as much high\norder accuracy as possible, even in simulations with very strong shocks, as≠.g. presented in the Sedov test. The framework retains the locality of the\nstandard DG scheme and is hence well suited for a combination with adaptive\nmesh refinement and parallel computing. The numerical tests demonstrate the\nsub-element adaptive behavior of the new shock capturing approach and its high\naccuracy.\n