Meteorology and Atmospheric Physics

, Volume 81, Issue 1, pp 129–135

The shallow water equations on the sphere and their Lagrange-Galerkin-solution

  • T. Heinze
  • A. Hense

DOI: 10.1007/s007030200034

Cite this article as:
Heinze, T. & Hense, A. Meteorol. Atmos. Phys. (2002) 81: 129. doi:10.1007/s007030200034


¶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.

Copyright information

© Springer-Verlag/Wien 2002

Authors and Affiliations

  • T. Heinze
    • 1
  • A. Hense
    • 2
  1. 1.Lehrstuhl für Numerische Mathematik und Wissenschaftliches Rechnen, Technische Universität München, GermanyDE
  2. 2.Meteorologisches Institut der Universität Bonn, GermanyDE