Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.
Philos Trans A Math Phys Eng Sci. 2009 Nov 28;367(1907):4483-96. doi: 10.1098/rsta.2009.0168.
The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the GeoClaw software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.
最近引入的用于球面上二维偏微分方程和球壳内三维问题的逻辑矩形有限体积网格具有几乎均匀的单元大小，避免了严重的柯朗数限制。我们使用 GeoClaw 软件展示了最近的自适应网格细化结果，并演示了精确保持平衡解的方法，例如在任意海底地形上处于静止状态的海洋的浅水方程。
