Solving the fully nonlinear weakly dispersive Serre equations for flows over dry beds,International Journal for Numerical Methods in Fluids

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Solving the fully nonlinear weakly dispersive Serre equations for flows over dry beds
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-06-08 , DOI: 10.1002/fld.4873
Jordan P.A. Pitt ₁ , Christopher Zoppou ₁ , Stephen G. Roberts ₁

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We describe a numerical method for solving the Serre equations that can simulate flows over dry bathymetry. The method solves the Serre equations in conservation law form with a finite volume method. A finite element method is used to solve the auxiliary elliptic equation for the depth‐averaged horizontal velocity. The numerical method is validated against the lake at rest analytic solution, demonstrating that it is well‐balanced. Since there are currently no known nonstationary analytical solutions to the Serre equation that involve bathymetry, a nonstationary forced solution, involving bathymetry was developed. The method was further validated and its convergence rate established using the developed nonstationary forced solution containing the wetting and drying of bathymetry. Finally, the method is also validated against experimental results for the run‐up of a solitary wave on a sloped beach. The finite‐volume finite‐element approach to solving the Serre equation was found to be accurate and robust.

中文翻译：

求解干床上的全非线性弱色散Serre方程

我们描述了一种求解Serre方程的数值方法，该方法可以模拟干式测深仪上的流量。该方法用有限体积法求解守恒律形式的Serre方程。使用有限元方法求解深度平均水平速度的辅助椭圆方程。该数值方法针对静止湖分析解决方案进行了验证，表明其平衡良好。由于目前尚无涉及测深法的Serre方程的非平稳解析解，因此开发了涉及测深法的非平稳强迫解。使用开发的包含测深仪的润湿和干燥的非平稳强迫溶液进一步验证了该方法并确定了收敛速度。最后，该方法还针对倾斜海滩上孤波传播的实验结果进行了验证。发现解决Serre方程的有限体积有限元方法是准确且稳健的。

更新日期：2020-06-08

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