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A robust second-order surface reconstruction for shallow water flows with a discontinuous topography and a Manning friction
Advances in Computational Mathematics ( IF 1.7 ) Pub Date : 2020-04-02 , DOI: 10.1007/s10444-020-09783-1
Jian Dong

A second-order surface reconstruction (SR) method for the shallow water equations with a discontinuous bottom topography and a Manning friction source term is presented. We redefine the water surface level at the cell interface by using the minimum difference between the bottom level and the original water surface level. The reconstructed water surface level is used to define the intermediate bottom level and the intermediate water height at the cell interface. We propose an explicit-implicit method to address the friction source term. The new second-order SR scheme together with the explicit-implicit method can preserve a special steady-state solution of the system and can maintain the positivity of the water depth. We also extend the new scheme to two-dimensional shallow water flows. To demonstrate the robustness and effectiveness of the new scheme, we use several classical numerical experiments for the shallow water flows over a complex bottom topography.

中文翻译:

具有不连续地形和曼宁摩擦的用于浅水流动的鲁棒二阶表面重建

提出了具有不连续底部地形和曼宁摩擦源项的浅水方程组的二阶表面重构(SR)方法。我们通过使用底部水位与原始水表面水位之间的最小差重新定义单元界面的水表面水位。重建的水面高度用于定义单元界面处的中间底部水位和中间水位。我们提出一种显式-隐式方法来解决摩擦源项。新的二阶SR方案与显式-隐式方法一起可以保留系统的特殊稳态解,并且可以保持水深的正值。我们还将新方案扩展到二维浅水流。
更新日期:2020-04-02
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