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Feng Zhou, Guoxian Chen, Sebastian Noelle and Huaicheng Guo A well-balanced stable generalized Riemann problem scheme for shallow water equations using adaptive moving unstructured triangular meshes International Journal for Numerical Methods in Fluids 73

Article first published online: 4 APR 2013 | DOI: 10.1002/fld.3800

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We propose a well-balanced stable generalized Riemann problem scheme for the shallow water equations with irregular bottom topography based on moving triangular meshes. Numerical tests show the accuracy, efficiency and robust of the scheme. In order to stabilize the computations near equilibria, we use the Rankine-Hugoniot condition to remove a singularity from the GRP solver. We develop a remapping onto the new mesh (after grid movement) based on equilibrium variables. This, together with already established techniques, guarantees the well-balancing. Numerical tests show the accuracy, efficiency, and robustness of the GRP moving mesh method: lake at rest solutions are preserved even when the underlying mesh is moving (e.g., mesh point are moved to regions of steep gradients) and various comparisons with fixed coarse and fine meshes demonstrate high resolution at relatively low cost.

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