Dynamically adaptive grid based discontinuous Galerkin shallow water model
Dynamically adaptive grid based discontinuous Galerkin shallow water model
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DOI：
10.1016/j.advwatres.2011.11.006
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发表时间：
2012-03
影响因子：
4.7
通讯作者：
G. Kesserwani;Q. Liang
中科院分区：
文献类型：
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作者：
G. Kesserwani;Q. Liang
本文建立了一个基于动态自适应四边形网格系统二维浅水方程局部平面龙格-库塔不连续伽辽金（RKDG2）解的godunov型数值模型，用于浅水波浪模拟，并特别应用于洪水模拟。为了与动态网格适应相一致，重新制定了平衡良好的RKDG2框架，以促进真实的洪水建模。网格自适应和流量数据的重新分配是基于简单的局部流量特性测量的自动化。使用一个分析和两个诊断测试用例来验证动态自适应RKDG2模型对基于均匀四边形网格的替代RKDG2代码的性能。然后，通过进一步将其应用于重现实验室规模的海啸基准案例和历史上的马尔帕塞特溃坝事件，对自适应模型进行了评估。数值证据表明，新算法能够充分地解决移动波特征，且计算成本远低于基于精细均匀网格的对应算法。
A Godunov-type numerical model, which is based on the local planar Runge–Kutta discontinuous Galerkin (RKDG2) solutions to the two dimensional (2D) shallow water equations (SWEs) on a dynamically adaptive quadrilateral grid system, is developed in this work for shallow water wave simulations, with particular application to flood inundation modeling. To be consistent with the dynamic grid adaptation, the well-balanced RKDG2 framework is reformulated to facilitate realistic flood modeling. Grid adaptation and redistribution of flow data are automated based on simple measures of local flow properties. One analytical and two diagnostic test cases are used to validate the performance of the dynamically adaptive RKDG2 model against an alternative RKDG2 code based on uniform quadrilateral meshes. The adaptive model is then assessed by further applying it to reproduce a laboratory-scale tsunami benchmark case and the historical Malpasset dam-break event. Numerical evidence indicates that the new algorithm is able to resolve the moving wave features adequately at much less computational cost than the refined uniform grid-based counterpart.