The shallow water equations on the sphere and their Lagrange-Galerkin-solution |
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| Authors: | T. Heinze A. Hense |
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| Affiliation: | Lehrstuhl für Numerische Mathematik und Wissenschaftliches Rechnen, Technische Universit?t München, Germany, DE
Meteorologisches Institut der Universit?t Bonn, Germany, DE
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| Abstract: | Summary ?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. Received April 13, 2001; Revised December 18, 2001 |
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