NCAS Climate, Department of Meteorology, University of Reading, Reading, UK.
Philos Trans A Math Phys Eng Sci. 2009 Nov 28;367(1907):4523-42. doi: 10.1098/rsta.2009.0151.
The shallow water equations are solved using a mesh of polygons on the sphere, which adapts infrequently to the predicted future solution. Infrequent mesh adaptation reduces the cost of adaptation and load-balancing and will thus allow for more accurate mapping on adaptation. We simulate the growth of a barotropically unstable jet adapting the mesh every 12 h. Using an adaptation criterion based largely on the gradient of the vorticity leads to a mesh with around 20 per cent of the cells of a uniform mesh that gives equivalent results. This is a similar proportion to previous studies of the same test case with mesh adaptation every 1-20 min. The prediction of the mesh density involves solving the shallow water equations on a coarse mesh in advance of the locally refined mesh in order to estimate where features requiring higher resolution will grow, decay or move to. The adaptation criterion consists of two parts: that resolved on the coarse mesh, and that which is not resolved and so is passively advected on the coarse mesh. This combination leads to a balance between resolving features controlled by the large-scale dynamics and maintaining fine-scale features.
浅水波方程组采用球面上的多边形网格进行求解，该网格对未来的预测解适应得并不频繁。不频繁的网格自适应可以降低自适应和负载平衡的成本，从而允许在自适应时进行更准确的映射。我们模拟了一个正压不稳定射流的增长，每 12 小时自适应一次网格。使用主要基于涡度梯度的自适应准则，得到的网格中大约有 20%的单元与均匀网格的单元相同，能够得到等效的结果。这与之前使用每 1-20 分钟自适应一次的相同测试案例的研究结果相似。网格密度的预测涉及在局部细化网格之前，在粗网格上求解浅水波方程组，以估计需要更高分辨率的特征将在哪里增长、衰减或移动。自适应准则由两部分组成：一部分在粗网格上求解，另一部分在粗网格上未被求解，因此被被动地平流。这种组合可以在由大尺度动力学控制的特征的分辨率和对小尺度特征的保持之间达到平衡。
