Development of a Multigrid-Scheme in order to Solve Elliptic Differential Equations on Massivly Parallel Computers and its Implementation in the LES Model PALM
Responsible: Jörg Uhlenbrock
Project type: Diplomarbeit (equivalent to master thesis)
Duration: 07/08/2000 - 06/08/2001

In the near future, computations with the LES-model PALM should also be done with an irregular (bottom) boundary condition (e.g. due to buildings). Thereafter, the modified model will be used for investigations of the tubulent flow structure in a simplified urban area. To solve the Boussinesq-approximated Navier-Stokes equations, the application of a so-called "pressure solver" is necessary after each timestep in the model, resulting in a windfield with no divergence. With regard to our model, the pressure solver is just a Poisson equation. In the actual model version the solution of the poisson equation is realized by a non-iterative procedure, based on Fast-Fourier Tansformation (FFT). But this method cannot be applied to an irregular boundary condition. For such a boundary, iterative procedures are more suitable, e.g. the Gauss-Seidel method. Furthermore, the iterative methods can easily be paralellized. Unfortunately, the convergence of these methods on large computational grids, as used by our model runs, is very slow. Therefore, the FFT has been the only practical method to solve the Poisson equation up to date. A realistic alternative is provided by the so-called multigrid method, which accelerates the convergence of iterative methods. The solution of the Poisson equation then becomes independent of grid size. The target of this thesis is to develop a parallelized version of such a multigrid method for solving the Poisson equation, and its implementation in PALM.