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A well‐balanced stable generalized Riemann problem scheme for shallow water equations using adaptive moving unstructured triangular meshes
Author(s) -
Zhou Feng,
Chen Guoxian,
Noelle Sebastian,
Guo Huaicheng
Publication year - 2013
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3800
Subject(s) - polygon mesh , shallow water equations , robustness (evolution) , degree rankine , riemann solver , solver , grid , computation , mathematics , mesh generation , computer science , mathematical optimization , geometry , algorithm , mathematical analysis , finite element method , finite volume method , mechanics , physics , biochemistry , chemistry , gene , quantum mechanics , thermodynamics
SUMMARY We propose a well‐balanced stable generalized Riemann problem (GRP) scheme for the shallow water equations with irregular bottom topography based on moving, adaptive, unstructured, triangular meshes. In order to stabilize the computations near equilibria, we use the Rankine–Hugoniot condition to remove a singularity from the GRP solver. Moreover, we develop a remapping onto the new mesh (after grid movement) based on equilibrium variables. This, together with the 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 points are moved to regions of steep gradients), and various comparisons with fixed coarse and fine meshes demonstrate high resolution at relatively low cost. Copyright © 2013 John Wiley & Sons, Ltd.