A high‐order PIC method for advection‐dominated flow with application to shallow water waves |
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| Authors: | W Wang DM Kelly |
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| Affiliation: | 1. Department of Mathematics and Statistics, Florida International University, Miami, FL, USA;2. Coastal Research Laboratory, International Hurricane Research Center, Florida International University, Miami, FL, USA |
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| Abstract: | A hybrid Eulerian‐Lagrangian particle‐in‐cell–type numerical method is developed for the solution of advection‐dominated flow problems. Particular attention is given over to the high‐order transfer of flow properties from the particles to the grid. For smooth flows, the method presented is of formal high‐order accuracy in space. The method is applied to solve the nonlinear shallow water equations resulting in a new, and novel, shock capturing shallow water solver. The approach is able to simulate complex shallow water flows, which can contain an arbitrary number of discontinuities. Both trivial and nontrivial bottom topography is considered, and it is shown that the new scheme is inherently well balanced, exactly satisfying the  ‐property. The scheme is verified against several one‐dimensional benchmark shallow water problems. These include cases that involve transcritical flow regimes, shock waves, and nontrivial bathymetry. In all the test cases presented, very good results are obtained. |
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| Keywords: | advection complex bathymetry Eulerian‐Lagrangian high order particle in cell shallow water equations shock waves well balanced |
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‐property. The scheme is verified against several one‐dimensional benchmark shallow water problems. These include cases that involve transcritical flow regimes, shock waves, and nontrivial bathymetry. In all the test cases presented, very good results are obtained.