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An $h$-Box Method for Shallow Water Equations Including Barriers
SIAM Journal on Scientific Computing ( IF 3.1 ) Pub Date : 2021-03-24 , DOI: 10.1137/19m128363x
Jiao Li , Kyle T. Mandli

SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page B431-B454, January 2021.
The shallow water equations provide the basic modeling equations for a number of coastal flooding hazards, such as tsunamis and storm surge. In realistic scenarios, there are often structures important to these flows that have a large extent but small width, including sea walls, berms, and harbor barriers. Explicit time stepping schemes, most often used for the shallow water equations, can then suffer from time step restrictions due to the CFL condition. In this article, we introduce an approach that side-steps these issues by allowing a barrier to have zero-width and to cut a cell arbitrarily without suffering from CFL restrictions. This is done by supplementing existing Riemann solvers and leveraging $h$-box and large time stepping methods. These methods preserve the properties of the Riemann solver and add negligible cost to the original solvers.


中文翻译:

包含障碍的浅水方程组的$ h $ -Box方法

SIAM科学计算杂志,第43卷,第2期,第B431-B454页,2021年1月。
浅水方程为海啸和风暴潮等许多沿海洪水灾害提供了基本的建模方程。在现实情况下,通常存在对这些水流很重要的结构,这些结构在很大程度上但宽度很小,包括海堤,堤坝和港口障碍物。显式时间步进方案(最常用于浅水方程式)会由于CFL条件而受到时间步长的限制。在本文中,我们介绍了一种方法,该方法通过使障碍物的宽度为零并任意切割一个单元而不受CFL的限制,从而避开了这些问题。这是通过补充现有的Riemann求解器并利用$ h $ -box和大量时间步进方法来完成的。
更新日期:2021-03-25
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