Institut für Mathematik, FB Mathematik and Informatik, Freie Universitaet Berlin, ,Berlin, Germany.
Philos Trans A Math Phys Eng Sci. 2009 Nov 28;367(1907):4559-75. doi: 10.1098/rsta.2009.0174.
Cut-cell meshes present an attractive alternative to terrain-following coordinates for the representation of topography within atmospheric flow simulations, particularly in regions of steep topographic gradients. In this paper, we present an explicit two-dimensional method for the numerical solution on such meshes of atmospheric flow equations including gravitational sources. This method is fully conservative and allows for time steps determined by the regular grid spacing, avoiding potential stability issues due to arbitrarily small boundary cells. We believe that the scheme is unique in that it is developed within a dimensionally split framework, in which each coordinate direction in the flow is solved independently at each time step. Other notable features of the scheme are: (i) its conceptual and practical simplicity, (ii) its flexibility with regard to the one-dimensional flux approximation scheme employed, and (iii) the well-balancing of the gravitational sources allowing for stable simulation of near-hydrostatic flows. The presented method is applied to a selection of test problems including buoyant bubble rise interacting with geometry and lee-wave generation due to topography.
切网格在表示大气流动模拟中的地形方面提供了一种有吸引力的替代地形跟随坐标的方法，特别是在地形梯度陡峭的区域。在本文中，我们提出了一种显式二维方法，用于在包括重力源的大气流动方程的这种网格上进行数值求解。该方法是完全守恒的，并允许由规则网格间距确定的时间步长，避免了由于任意小的边界单元而导致的潜在稳定性问题。我们相信该方案是独特的，因为它是在一个维度分裂的框架内开发的，其中在每个时间步中独立求解流中的每个坐标方向。该方案的其他显著特点是：(i)其概念和实际的简单性，(ii)对所采用的一维通量逼近方案的灵活性，以及(iii)对重力源的良好平衡，允许对近静压流动进行稳定模拟。所提出的方法应用于一系列测试问题，包括与几何形状相互作用的浮力气泡上升和地形引起的背风波生成。
