Parallelisation of algorithms for advection diffusion problems

The numerical algorithm in the simulation package TRIWAQ is analysed for inherent parallelism. One equation solver that is used for the discretised momentum equations appears to be purely sequential. A comparison with alternative solvers for an advection diffusion test problem indicates however that it is extremely effective on a sequential computer. For larger Courant numbers only the block Jacobi method has a comparable number of iterations, but it requires more work per iteration. From this analysis we draw conclusions on the parallelisation of algorithms. First of all, the use of automatic parallelisation tools is limited here. The problem is that the algorithm must be modified, which cannot be done by a compiler. If the solver is replaced, one must be aware of parallel and numerical efficiency. It is argued that instead of modifying only the equation solver it is better to reconsider all choices in the development of the numerical method, such as the structure of the integration scheme.