Adaptive finite volume methods with well‐balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam‐break flood (France, 1959)
Adaptive finite volume methods with well‐balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam‐break flood (France, 1959)
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DOI：
10.1002/fld.2298
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发表时间：
2011-07
影响因子：
1.8
通讯作者：
D. George
中科院分区：
文献类型：
--
作者：
D. George
本文描述并验证了采用平衡高分辨率有限体积法和块结构动态自适应网格细化（AMR）方法求解浅水方程，在崎岖地形上模拟前进的洪水波。块结构AMR的效率使得大规模问题易于处理，并且允许使用精确和稳定的方法来解决四边形网格上的一般双曲问题。在崎岖的地形中，洪水的特征表明，如前进的干湿锋面和由于来自可变地形的平衡源项而产生的非平稳稳定状态，提出了独特的挑战，需要特殊的黎曼解算器等修改。在这种情况下，测试了一个用于淹没和地形上一般（非平稳）流动的平衡良好的黎曼解算器。本文介绍了在崎岖地形中模拟洪水的困难，以及使用AMR和均衡方法的基本原理和有效性。通过模拟Malpasset溃坝洪水（法国，1959年）验证了算法的有效性，该算法以前曾作为基准问题。给出了历史现场数据、实验室模型数据和其他数值模拟结果（在静态拟合网格上计算）进行比较。这些方法是在GEOCLAW中实现的，GEOCLAW是开源CLAWPACK软件的一个子集。所有的软件都可以在www.clawpack.org上免费获得。2010年由John Wiley & Sons出版。
The simulation of advancing flood waves over rugged topography, by solving the shallow‐water equations with well‐balanced high‐resolution finite volume methods and block‐structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block‐structured AMR makes large‐scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet–dry fronts and non‐stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well‐balanced Riemann solver for inundation and general (non‐stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well‐balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam‐break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in GEOCLAW, a subset of the open‐source CLAWPACK software. All the software is freely available at www.clawpack.org. Published in 2010 by John Wiley & Sons, Ltd.