当前位置: X-MOL 学术J. Comput. Phys. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A Well-Balanced Central-Upwind Scheme for the Thermal Rotating Shallow Water Equations
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2020-03-24 , DOI: 10.1016/j.jcp.2020.109414
Alexander Kurganov , Yongle Liu , Vladimir Zeitlin

We develop a well-balanced central-upwind scheme for rotating shallow water model with horizontal temperature and/or density gradients—the thermal rotating shallow water (TRSW). The scheme is designed using the flux globalization approach: first, the source terms are incorporated into the fluxes, which results in a hyperbolic system with global fluxes; second, we apply the Riemann-problem-solver-free central-upwind scheme to the rewritten system. We ensure that the resulting method is well-balanced by switching off the numerical diffusion when the computed solution is near (at) thermo-geostrophic equilibria.

The designed scheme is successfully tested on a series of numerical examples. Motivated by future applications to large-scale motions in the ocean and atmosphere, the model is considered on the tangent plane to a rotating planet both in mid-latitudes and at the Equator. The numerical scheme is shown to be capable of quite accurately maintaining the equilibrium states in the presence of nontrivial topography and rotation. Prior to numerical simulations, an analysis of the TRSW model based on the use of Lagrangian variables is presented, allowing one to obtain criteria of existence and uniqueness of the equilibrium state, of the wave-breaking and shock formation, and of instability development out of given initial conditions. The established criteria are confirmed in the conducted numerical experiments.



中文翻译:

热旋转浅水方程组的平衡良好的上风向方案

我们为具有水平温度和/或密度梯度的旋转浅水模型(热旋转浅水(TRSW))开发了一种平衡良好的中央逆风方案。该方案是使用通量全球化方法设计的:首先,将源项合并到通量中,从而形成具有全局通量的双曲系统;第二,我们将无黎曼问题求解器的中央逆风方案应用于重写的系统。当计算的解接近于(地)热地转平衡时,我们通过关闭数值扩散来确保所得到的方法具有良好的平衡。

所设计的方案已通过一系列数值示例成功测试。受未来应用在海洋和大气中大规模运动的推动,该模型在中纬度和赤道处与旋转行星的切线平面上均被考虑。数值方案显示出能够在存在非平凡的形貌和旋转的情况下非常准确地保持平衡状态。在进行数值模拟之前,先对基于拉格朗日变量的TRSW模型进行了分析,从而使人们能够获得平衡态存在,唯一性,破裂和激波形成以及不稳定发展的标准。给定初始条件。建立的标准在进行的数值实验中得到证实。

更新日期:2020-03-26
down
wechat
bug