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arXiv · 1809.09815

Analysis and entropy stability of the line-based discontinuous Galerkin method

Will Pazner·Per-Olof Persson
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Abstract

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stability property is important for the robustness of the method, in particular when applied to problems with discontinuous solutions or when the mesh is under-resolved. This line-based method is significantly less computationally expensive than a standard DG method. Numerical results are shown demonstrating the effectiveness of the method on a variety of test cases, including Burgers' equation and the Euler equations, in one, two, and three spatial dimensions.

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Will Pazner, Per-Olof Persson. 2018-09-26. Analysis and entropy stability of the line-based discontinuous Galerkin method. https://doi.org/10.1007/s10915-019-00942-1

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