High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers
High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers
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DOI：
10.1016/j.jcp.2022.111255
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
Guanlan Huang;Y. Xing;T. Xiong
中科院分区：
文献类型：
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作者：
Guanlan Huang;Y. Xing;T. Xiong
本文提出了非平底地形浅水方程的高阶半隐式良好平衡渐近保持有限差分WENO格式。我们认为弗劳德数在O(1)到0的范围内，在零弗劳德极限下成为无重力波平衡流动的“湖方程组”。我们采用了平衡的有限差分WENO重构，以及高精度的隐式-显式(IMEX)Runge-Kutta时间离散化。所得到的半隐式格式具有良好的平衡性、渐近保持(AP)和渐近精度(AA)。给出了一维和二维数值结果，验证了所提方法的高阶精度、AP性质和捕捉定态解的小扰动的良好性能。
In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider the Froude number ranging from O (1) to 0, which in the zero Froude limit becomes the “lake equations” for balanced flow without gravity waves. We apply a well-balanced finite difference WENO reconstruction, coupled with a stiffly accurate implicit-explicit (IMEX) Runge-Kutta time discretization. The resulting semi-implicit scheme can be shown to be well-balanced, asymptotic preserving (AP) and asymptotically accurate (AA) at the same time. Both one-and two-dimensional numerical results are provided to demonstrate the high order accuracy, AP property and good performance of the proposed methods in capturing small perturbations of steady state solutions.