Entropy stable hydrostatic reconstruction schemes for shallow water systems
<|reference_start|>Entropy stable hydrostatic reconstruction schemes for shallow water systems: In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite volume scheme and combine it with entropy conservative fluxes and suitable numerical dissipation to preserve an entropy inequality in the semi-discrete case. We then combine the novel hydrostatic reconstruction with a collocated nodal split-form discontinuous Galerkin spectral element method, extending the method to high-order and curvilinear meshes. The high-order method incorporates an additional positivity-limiter and is blended with a compatible subcell finite volume method to maintain well-balancedness at wet/dry fronts. We prove entropy stability, well-balancedness, and positivity-preservation for both methods. Numerical results for the high-order method validate the theoretical findings and demonstrate the robustness of the scheme.<|reference_end|>
@article{ersing2024entropy,
    title={Entropy stable hydrostatic reconstruction schemes for shallow water
  systems},
    author={Patrick Ersing, Sven Goldberg, Andrew R. Winters},
    journal={arXiv preprint arXiv:2406.14119},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.14119},
    primaryClass={math.NA cs.NA}
}