Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
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DOI：
10.4208/cicp.220210.020710a
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发表时间：
2011-08
期刊：
影响因子：
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通讯作者：
A. Bollermann;S. Noelle;Maria Luk'avcov'a - Medvidov'a
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文献类型：
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作者：
A. Bollermann;S. Noelle;Maria Luk'avcov'a - Medvidov'a
我们提出了一种新的有限体积演化伽辽金（FVEG）方案，用于求解以底部地形作为源项的浅水方程（SWE）。我们的新方案将基于 (Luk\'a\v{c}ov\'a, Noelle and Kraft, J. Comp. Phys. 221, 2007) 中提出的 FVEG 方法，但增加了处理干燥边界的可能性。最重要的方面是保持水位高度的积极性。我们提出了一种通用方法来确保任意有限体积方案的这一点。主要思想是限制细胞的输出通量，只要它们会产生负水高度。从物理上讲，这对应于真空下不存在通量。然后通过分裂通量的重力部分和重力驱动部分来重新建立良好的平衡。此外，还引入了新的熵修正，可以改善声波稀疏波的再现。
We present a new Finite Volume Evolution Galerkin (FVEG) scheme for the solution of the shallow water equations (SWE) with the bottom topography as a source term. Our new scheme will be based on the FVEG methods presented in (Luk\'a\v{c}ov\'a, Noelle and Kraft, J. Comp. Phys. 221, 2007), but adds the possibility to handle dry boundaries. The most important aspect is to preserve the positivity of the water height. We present a general approach to ensure this for arbitrary finite volume schemes. The main idea is to limit the outgoing fluxes of a cell whenever they would create negative water height. Physically, this corresponds to the absence of fluxes in the presence of vacuum. Well-balancing is then re-established by splitting gravitational and gravity driven parts of the flux. Moreover, a new entropy fix is introduced that improves the reproduction of sonic rarefaction waves.