The shallow water equations on the sphere and their Lagrange-Galerkin-solution
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- Heinze, T. & Hense, A. Meteorol. Atmos. Phys. (2002) 81: 129. doi:10.1007/s007030200034
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¶The shallow water equations are formulated on the sphere in a three-dimensional coordinate system with the aid of tangential velocity components and differential operators. We introduce a modified semi-Lagrangian scheme for the discretization in time. The discretization in space is solved by linear finite elements. The grids we use are regular refinements of a macro triangulation which itself is derived from a highly symmetric polyeder also known as a bucky or soccer ball. The good numerical results show that this combination is a promising approach. The numerical algorithm is stable and its strength is the conservation of mass and energy.