A discontinuous Galerkin algorithm for the two-dimensional shallow water equations
A discontinuous Galerkin algorithm for the two-dimensional shallow water equations
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DOI：
10.1016/j.cma.2010.07.007
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发表时间：
2010-12
影响因子：
7.2
通讯作者：
G. Kesserwani;Q. Liang
中科院分区：
文献类型：
--
作者：
G. Kesserwani;Q. Liang
本文提出了一种新的高分辨率有限元格式，通过局部平面近似求解二维浅水波方程。河床地形数据以与流量变量相同的方式局部近似，以呈现本能的良好平衡方案。有限体积（FV）的润湿和干燥技术，重建黎曼状态，确保非负水深和保持平衡的解决方案进行调整，并在当前的有限元框架实施。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。单元间通量采用HLLC近似黎曼解进行迎风计算。通过稳定隐式离散有限元逼近系数的摩擦力单独评估。边界条件推导和报告的细节。本模型验证了几个测试用例，包括溃坝流的规则和不规则域的洪水和干燥。
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.