Spherical shallow‐water wave simulation by a cubed‐sphere finite‐difference solver,Quarterly Journal of the Royal Meteorological Society

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Spherical shallow‐water wave simulation by a cubed‐sphere finite‐difference solver
Quarterly Journal of the Royal Meteorological Society ( IF 3.0 ) Pub Date : 2020-11-15 , DOI: 10.1002/qj.3946
M. Brachet ₁ , J.‐P. Croisille ₂

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We consider the test suite for the shallow‐water (SW) equations on the sphere suggested by Paldor in earlier work. This series of tests consists of zonally propagating wave solutions on the full sphere. Two series of solutions are considered. The first series is referred to as “barotropic". It consists of an extension of the Rossby–Haurwitz test case. The second series, referred to as “baroclinic”, consists of a generalisation of the Matsuno solution to the linearized SW equations in an equatorial channel. The Hermitian Compact Cubed Sphere (HCCS) model which is used in this paper is a recently introduced SW solver on the sphere. The spatial approximation is a centred finite‐difference scheme based on high‐order differencing along great circles. The time stepping is performed by the explicit RK4 scheme or by an exponential scheme. For both barotropic and baroclinic test case series, the results show a very good agreement of the numerical solution with the analytic one, even for long time simulations.

中文翻译：

用立方球体有限差分求解器模拟球形浅水波

我们考虑帕尔多（Paldor）在早期工作中建议的球体浅水（SW）方程的测试套件。这一系列的测试由整个球面上的区域传播波解组成。考虑了两个系列的解决方案。第一个系列称为“正压”，包括对Rossby–Haurwitz测试用例的扩展；第二个系列称为“斜压”，包括对线性方程组中的线性SW方程的Matsuno解的推广。赤道通道：本文使用的埃尔米特紧凑立方球面（HCCS）模型是最近在球面上引入的SW解算器，空间逼近是基于沿大圆的高阶微分的中心有限差分方案。步进是通过显式RK4方案或指数方案执行的。

更新日期：2020-11-15

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