Well-balanced numerical resolution of the two-layer shallow water equations under rigid-lid with wet–dry fronts
In this paper, we present a well-balanced numerical scheme for the frictional two-layer shallow water equations (2LSWE) over variable bottom topography and under a rigid-lid (RL) to simulate internal waves propagating over wet and dry areas. Following the idea of Liang and Borthwick (2009) for the d...
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| المؤلف الرئيسي: | |
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| التنسيق: | article |
| منشور في: |
2022
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| الوصول للمادة أونلاين: | http://hdl.handle.net/10725/16615 https://doi.org/10.1016/j.compfluid.2021.105277 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://www.sciencedirect.com/science/article/pii/S0045793021003704 |
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| الملخص: | In this paper, we present a well-balanced numerical scheme for the frictional two-layer shallow water equations (2LSWE) over variable bottom topography and under a rigid-lid (RL) to simulate internal waves propagating over wet and dry areas. Following the idea of Liang and Borthwick (2009) for the derivation of a pre-balanced formulation for one-layer flows, we derive a new formulation of the 2LSWE-RL using the interface elevation above datum and horizontal momentum as conservative variables. This new formulation mathematically balances the flux gradient and source terms so that the lake-at-rest steady state is automatically preserved in wet-bed applications. A proper discretization of the slope source term is adopted to produce well-balanced solutions in dry-bed areas where the lower layer depth vanishes. Using the Harten, Lax, and van Leer (HLL) approximate Riemann solver, we adopt a finite volume MUSCL-RK2 method to construct a second-order well-balanced numerical scheme ensuring the non-negativity of the layers depths with a special treatment of source terms. Finally, various numerical experiments are tested |
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