On the robustness of high-order upwind summation-by-parts methods for nonlinear conservation laws
arxiv(2023)
摘要
We use the framework of upwind summation-by-parts (SBP) operators developed
by Mattsson (2017, doi:10.1016/j.jcp.2017.01.042) and study different flux
vector splittings in this context. To do so, we introduce
discontinuous-Galerkin-like interface terms for multi-block upwind SBP methods
applied to nonlinear conservation laws. We investigate the behavior of the
upwind SBP methods for flux vector splittings of varying complexity on
Cartesian as well as unstructured curvilinear multi-block meshes. Moreover, we
analyze the local linear/energy stability of these methods following Gassner,
Svärd, and Hindenlang (2022, doi:10.1007/s10915-021-01720-8). Finally, we
investigate the robustness of upwind SBP methods for challenging examples of
shock-free flows of the compressible Euler equations such as a Kelvin-Helmholtz
instability and the inviscid Taylor-Green vortex.
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