Tsunami modelling with adaptively refined finite volume methods
Tsunami modelling with adaptively refined finite volume methods
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DOI：
10.1017/s0962492911000043
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发表时间：
2011-01-01
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影响因子：
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通讯作者：
Berger, Marsha J.
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文献类型：
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作者：
LeVeque, Randall J.;George, David L.;Berger, Marsha J.
跨洋海啸传播的数值模拟，以及小范围沿海地区淹没的详细模拟，对算法提出了许多挑战。深度平均浅水方程可以将其简化为两个空间维度上的时间相关问题，但即使如此，为了有效处理空间尺度上的巨大差异，使用自适应网格细化也是至关重要的。这必须以一种“平衡良好”的方式来完成，这种方式必须准确地捕捉到对静止海洋稳定状态的非常小的扰动。淹没可以通过允许细胞从干到湿的动态变化来建模，但这也必须在细化边界附近仔细完成。我们在基于riemann - solators的海啸建模有限体积方法的背景下讨论这些问题。使用GeoClaw软件给出了几个例子，并提供了示例代码。所讨论的技术也适用于各种其他地球物理流动。
Numerical modelling of transoceanic tsunami propagation, together with the detailed modelling of inundation of small-scale coastal regions, poses a number of algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this to a time-dependent problem in two space dimensions, but even so it is crucial to use adaptive mesh refinement in order to efficiently handle the vast differences in spatial scales. This must be done in a 'well-balanced' manner that accurately captures very small perturbations to the steady state of the ocean at rest. Inundation can be modelled by allowing cells to dynamically change from dry to wet, but this must also be done carefully near refinement boundaries. We discuss these issues in the context of Riemann-solver-based finite volume methods for tsunami modelling. Several examples are presented using the GeoClaw software, and sample codes are available to accompany the paper. The techniques discussed also apply to a variety of other geophysical flows.