Abstract

Uniformly third Order conserving Schems on Polygonal Grids. The interest in polygonal grids is increasing. They are an alternative to the more commonly used spectral and latitude longitude grids. Among other advantages they offer the possibility of a rather uniform cover of the sphere with grid cells. Other advantages concern the ease of using multiprocessing computers and using special vertical treatments, such as shaved cells. Well known examples of polygonal grids are the cube sphere and the icosahedral grid. After initial research by Sadourny and Williamsson the practicability of this approach was shown by Baumgardner and Steppeler. In particular Baumgardner showed that problems with some approaches can be traced back to the fact that for slightly irregular resolution methods are not uniformly second order. After correcting this problem Baumgardner was able to show that problems arising from irregular grids do not occur. Steppeler generalized this approach to third order. Both Baumgardners and Steppelers approaches were non conser ving. A generalization to conserving schemes will be presented and computational examples given. Another high order approach is the pecral element method, which currently is available for orders 4 an higher only. The approach presented can be considered as a version of third order spectral elements. The advantages of third order schemes over even higher order approaches will be discussed.