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A discontinuous Galerkin algorithm for the two-dimensional shallow water equations

机译：二维浅水方程组的不连续Galerkin算法

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A new high-resolution finite element scheme is introduced for solving the two-dimensional (2D) depth-integrated shallow water equations (SWE) via local plane approximations to the unknowns. Bed topography data are locally approximated in the same way as the flow variables to render an instinctive well-balanced scheme. A finite volume (FV) wetting and drying technique that reconstructs the Riemann states by ensuring non-negative water depth and maintaining well-balanced solution is adjusted and implemented in the current finite element framework. Meanwhile, a local slope-limiting process is applied and those troubled-slope-components are restricted by the minmod FV slope limiter. The inter-cell fluxes are upwinded using the HLLC approximate Riemann solver. Friction forces are separately evaluated via stable implicit discretization to the finite element approximating coefficients. Boundary conditions are derived and reported in details. The present model is validated against several test cases including dam-break flows on regular and irregular domains with flooding and drying.
机译：引入了一种新的高分辨率有限元方案，用于通过对未知数的局部平面近似来求解二维（2D）深度积分浅水方程（SWE）。床地形数据以与流量变量相同的方式进行局部逼近，以提供本能的良好平衡方案。在当前的有限元框架中，调整并实现了通过确保非负水深并保持平衡的溶液来重构黎曼状态的有限体积（FV）润湿和干燥技术。同时，应用局部斜率限制过程，并通过minmod FV斜率限制器限制那些有问题的斜率分量。使用HLLC近似Riemann求解器使单元间通量上风。摩擦力通过稳定的隐式离散化方法评估为有限元近似系数。得出边界条件并详细报告。本模型针对多个测试案例进行了验证，其中包括在规则和不规则区域上的洪水冲断和干燥过程中的溃坝水流。

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