Well-balanced numerical method for atmospheric flow equations with gravity
Well-balanced numerical method for atmospheric flow equations with gravity
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DOI：
10.1016/j.amc.2022.127587
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发表时间：
2023-02
期刊：
影响因子：
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通讯作者：
Alina Chertock;A. Kurganov;Tong Wu;Jun Yan
中科院分区：
文献类型：
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作者：
Alina Chertock;A. Kurganov;Tong Wu;Jun Yan
我们感兴趣的是在不规则区域中模拟由可压缩欧拉方程控制的重力分层大气流动。在这种模拟中，当在笛卡尔网格上进行计算时，会出现一个挑战。与不规则边界相交的规则矩形网格的使用导致在域的边界附近生成任意小且高度扭曲的计算单元。这种单元的出现可能会影响数值方法的稳定性和效率，因此需要特别注意，为了克服这一困难，我们引入了一个结构化的四边形网格，这是专为手头的不规则区域，并使用二阶中心迎风格式求解所研究的大气流动方程。此外，由此产生的数值方法的开发，以提供一个平衡的离散化的基础系统。后者是通过重写的控制方程的平衡变量表示已知的背景平衡态的扰动。所提出的方法进行了测试，在一些数值实验，包括浮泡上升和相互作用的（齐柏林飞艇）障碍物和由于地形的Lee波生成。所得到的数值结果表明所提出的计算方法的高分辨率和鲁棒性。
We are interested in simulating gravitationally stratified atmospheric flows governed by the compressible Euler equations in irregular domains. In such simulations, one of the challenges arises when the computations are conducted on a Cartesian grid. The use of regular rectangular grids that intersect with the irregular boundaries leads to the generation of arbitrarily small and highly distorted computational cells adjacent to the boundaries of the domain. The appearance of such cells may affect both the stability and efficiency of the numerical method and therefore require special attention.In order to overcome this difficulty, we introduce a structured quadrilateral mesh, which is designed for the irregular domain at hand, and solve the studied atmospheric flow equations using a second-order central-upwind scheme. In addition, the resulting numerical method is developed to provide a well-balanced discretization of the underlying system. The latter is achieved by rewriting the governing equations in terms of equilibrium variables representing perturbations of the known background equilibrium state. The proposed method is tested in a number of numerical experiments, including the buoyant bubble rising and interacting with an (zeppelin) obstacle and the Lee wave generation due to topography. The obtained numerical results demonstrate high resolution and robustness of the proposed computational approach.