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首页> 外文期刊>Journal of Computational Physics >Discontinuous Galerkin solver for the shallow-water equations in covariant form on the sphere and the ellipsoid
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Discontinuous Galerkin solver for the shallow-water equations in covariant form on the sphere and the ellipsoid

机译：球体和椭圆体的协调形式的浅水方程的不连续的Galerkin求解器

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摘要

A Discontinuous Galerkin (DG) method for the solution of the shallow-water equations (SWE) on arbitrary 2-dimensional (2D) manifolds is presented. To this purpose the SWE are formulated in covariant form using tensor notation. This allows to correctly transform the numerical fluxes between the local coordinate systems of any two neighboringgrid cells. In particular, the covariant form of the numerical diffusion term in the Lax-Friedrichs numerical flux has been derived, too. This general approach has the advantage that it avoids any coordinate singularity. It is tested for the SWE on the sphere with several standard test setups. Beyond this, a recently published test case with an analytic solution for linear inertial-gravity wave expansion has been performed. The derived formalism on arbitrary 2D manifolds allows an easy extension from the sphere to the ellipsoid. The comparison of a barotropic instability test case for the earth shows a non-negligible difference between the solution on these two bodies. The presented approach may be a starting point for the development of a dynamical core for numerical weather and climate prediction models based on the DG method. (C) 2020 Elsevier Inc. All rights reserved.
机译：提出了一种用于浅水方程（SWE）对任意二维（2D）歧管的浅水方程（SWE）的不连续的Galerkin（DG）方法。为此目的，SWE使用张量符号以协助形式配制。这允许在任何两个相邻格子电池的局部坐标系之间正确转换数值磁通量。特别地，LAX-Friedrichs数值通量中的数值扩散术语的协调形式也得到了衍生。这种通用方法具有避免任何坐标奇点的优点。它是用几个标准测试设置的球体上的SWE测试。除此之外，已经进行了最近公开的测试用例，具有用于线性惯性重力波扩展的分析解决方案。任意2D歧管上的衍生形式主义允许从球体到椭圆体的易于延伸。地球的波高调不稳定性测试箱的比较显示了这两个体上溶液之间的不可忽略的差异。所提出的方法可以是基于DG方法的用于数值天气和气候预测模型的动态核心开发的起点。 （c）2020 Elsevier Inc.保留所有权利。

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