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

Saturday, January 25th, 1997

A multilevel pressure solver for flows around buildings

A discretization of the $grad$ and $div$ operators on a cartesian grid are given as a part of an incompressible Navier--Stokes--Solver for the computation of flow patterns around buildings. The buildings are described on a three--dimensional cartesian grid by dividing the cartesian cells in three groups, free cells, body cells, and cut cells. Cut cells which are partially intersected by a building are characterized by the free volume part of the cell and the free area part of each of its six faces. For a cell centered piecewise constant pressure and a staggered arrangement of the velocity components the discretization of both operators is constructed by the use of the cut cell information and analog information on the shifted grids. The pressure correction is then computed on a sequence of nested cartesian grids where the operators are constructed for each grid level.

We compare a cascadic CG-like method and V--cycle multigrid algorithm for different building configurations.