IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows
IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows
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DOI：
10.4208/cicp.040413.160114a
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发表时间：
2014-08
影响因子：
3.7
通讯作者：
Georgij Bispen;K. R. Arun;M. Lukáčová-Medvid’ová;Sebastian Noelle
中科院分区：
文献类型：
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作者：
Georgij Bispen;K. R. Arun;M. Lukáčová-Medvid’ová;Sebastian Noelle
本文提出了一种新的求解低弗劳德数限制下浅水流动的大时间步长方法。为了考虑到多尺度现象，通常出现在地球物理流的非线性通量分为一个线性的部分，控制引力波和非线性平流。我们建议通过真正的多维演化算子来隐式地逼近时间和空间中的快速线性波。另一方面，我们通过特征线方法或一些标准的数值通量函数在时间和空间上显式地近似非线性平流部分。时间积分采用隐式-显式（IMEX）方法。我们应用IMEX Euler格式，两步Runge Kutta Cranck Nicolson格式，以及半隐式BDF格式，并证明了它们在低Froude数极限下的渐近保持性。数值实验表明，这些新的大时间步长有限体积格式的稳定性，精度和鲁棒性对小弗劳德数。
We present new large time step methods for the shallow water flows in the low Froude number limit. In order to take into account multiscale phenomena that typically appear in geophysical flows nonlinear fluxes are split into a linear part governing the gravitational waves and the nonlinear advection. We propose to approximate fast linear waves implicitly in time and in space by means of a genuinely multidimensional evolution operator. On the other hand, we approximate nonlinear advection part explicitly in time and in space by means of the method of characteristics or some standard numerical flux function. Time integration is realized by the implicit-explicit (IMEX) method. We apply the IMEX Euler scheme, two step Runge Kutta Cranck Nicolson scheme, as well as the semi-implicit BDF scheme and prove their asymptotic preserving property in the low Froude number limit. Numerical experiments demonstrate stability, accuracy and robustness of these new large time step finite volume schemes with respect to small Froude number.