Development of an efficient wetting and drying treatment for shallow‐water modeling using the quadrature‐free Runge‐Kutta discontinuous Galerkin method,International Journal for Numerical Methods in Fluids

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Development of an efficient wetting and drying treatment for shallow‐water modeling using the quadrature‐free Runge‐Kutta discontinuous Galerkin method
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-06-25 , DOI: 10.1002/fld.4884
Longxiang Li _{1,

2} , Qinghe Zhang ₁

Affiliation

To develop a robust, well‐balanced and quadrature‐free Runge‐Kutta discontinuous Galerkin (RKDG) shallow water solver, we introduce an efficient wetting and drying (WD) treatment in this paper. The main feature of this WD treatment is the use of vertex‐based linear reconstructed solutions in transition (partially wet) regions and high‐order solutions in smooth wet areas. To preserve the positivity of water depth, we also propose a modified time step size with the quadrature‐free scheme. The advantages of the WD treatment include robustness and the capability to address arbitrary high‐order RKDG methods in wet regions, thus making the quadrature‐free scheme more accurate and applicable to various flooding and drying problems. Two numerical test cases are used to validate the numerical method, and the results indicate that the WD method is accurate and robust for different flow regimes with dry areas.

中文翻译：

使用无正交Runge-Kutta不连续Galerkin方法开发用于浅水建模的有效润湿和干燥处理

为了开发一种坚固，平衡且无正交的Runge-Kutta不连续Galerkin（RKDG）浅水溶解器，我们在本文中引入了一种有效的湿润和干燥（WD）处理方法。WD处理的主要特征是在过渡（部分潮湿）区域中使用基于顶点的线性重构解决方案，并在光滑潮湿区域中使用高阶解决方案。为了保持水深的正值，我们还提出了采用无正交方案的修改后的时间步长。WD处理的优点包括鲁棒性和能够处理潮湿区域中任意高阶RKDG方法的能力，从而使无正交方案更加准确，适用于各种洪水和干燥问题。使用两个数值测试案例来验证数值方法，

更新日期：2020-06-25

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