References & Citations
Mathematics > Numerical Analysis
Title: High-order upwind summation-by-parts methods for nonlinear conservation laws
(Submitted on 23 Nov 2023 (this version), latest version 26 Mar 2024 (v2))
Abstract: High-order methods for conservation laws can be very efficient, in particular on modern hardware. However, it can be challenging to guarantee their stability and robustness, especially for under-resolved flows. A typical approach is to combine a well-working baseline scheme with additional techniques to ensure invariant domain preservation. To obtain good results without too much dissipation, it is important to develop suitable baseline methods. In this article, we study upwind summation-by-parts operators, which have been used mostly for linear problems so far. These operators come with some built-in dissipation everywhere, not only at element interfaces as typical in discontinuous Galerkin methods. At the same time, this dissipation does not introduce additional parameters. We discuss the relation of high-order upwind summation-by-parts methods to flux vector splitting schemes and investigate their local linear/energy stability. Finally, we present some numerical examples for shock-free flows of the compressible Euler equations.
Submission history
From: Hendrik Ranocha [view email][v1] Thu, 23 Nov 2023 10:19:14 GMT (4954kb,D)
[v2] Tue, 26 Mar 2024 19:22:33 GMT (5950kb,D)
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