Collection of abstracts 13th GAMM-Seminar Kiel on Numerical Treatment of Multi-Scale Problems January 24th to 26th, 1997.

Saturday, January 25th, 1997

Atmospheric Flows on Locally Refined Grids

Meshes for discretizing anelastic atmospheric transport equations should allow variable cell sizes (in horizontal and vertical direction) to include processes acting on different scales. Currently used (uniform) meshes permit vertical layers of different thicknesses and differing mesh width's for each horizontal layer.

Sometimes a better spatial resolution is needed (because of large gradients of emissions or surface, for example). In these cases smoothed locally refined grids in terrain--following coordinates are adequate. One cell may have more than one neighbour cell in each direction, then. Suitable data structures and schemes for discretization have been developed for such meshes. Those schemes have to be exact at least for constant pressure and velocity fields and have to conserve mass. This can be achieved by a suitable coarsening of the data given at the finest level of discretization (e.g. surface data and terms describing the coordinate transformation) and by suitable discretization at faces belonging to cells of different sizes.