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Finite Difference Approximation to the Shallow Water Equations on a Quasi-Uniform Spherical Grid

机译:拟均匀球面网格上浅水方程的有限差分逼近

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A new gridding technique for the solution of partial differential equations in spherical geometry is applied to the shallow water equations. The method, named the 'Cubed-Sphere', is based on a decomposition of the sphere into six identical regions, obtained by projecting the sides of a circumscribed cube onto a spherical surface. The grids defined on each of the six regions are coupled through an interopola-tion procedure based on the composite mesh finite difference method. We present results from two test cases: the integration of a steady state zonal geostrophic flow and the evolution of a Rossby-Haurwitz wave. For this latter case, the performance of the 'Cubed-Sphere' method will also be compared in terms of accuracy and execution time to those obtained using the spectral transform method. Finally, for the Rossby-Haurwitz test case we also give performance and scalability results obtained with a parallel version of the 'Cubed-Sphere' method run on a 25 Gflops (512 nodes) APE100/Quadrics massively parallel computer.
机译:将一种新的网格技术用于求解球面几何中的偏微分方程,并将其应用于浅水方程。该方法称为“立方球体”,它基于将球体分解为六个相同的区域的方法,该方法是将外接立方体的侧面投影到球形表面上而获得的。定义在六个区域中每个区域上的网格通过基于复合网格有限差分法的互操作过程进行耦合。我们介绍了两个测试案例的结果:稳态带状地转流的整合和Rossby-Haurwitz波的演化。对于后一种情况,还将在准确性和执行时间方面将“立方球面”方法的性能与使用光谱变换方法获得的性能进行比较。最后,对于Rossby-Haurwitz测试用例,我们还提供了在25 Gflops(512节点)APE100 / Quadrics大规模并行计算机上运行的并行版本的“ Cubed-Sphere”方法所获得的性能和可伸缩性结果。

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