Computational Model for Three-Dimensional Shallow Water Flows on the ALLIANT FX/4

摘要

Numerical methods for the simulation of three-dimensional water flows require a very great computational effort. Therefore, numerical methods should exploit the full potential of vector and parallel computers. The report deals with the efficient implementation on vector and parallel computers of a numerical method for the simplified three-dimensional shallow water equations. It contains the mathematical model and a brief description of the numerical method. The method results in the solution of a large number of tridiagonal systems. It goes on to describe two possible methods for the solution of these systems. The performance of these two methods has been tested on the ALLIANT FX/4. For the most efficient method, it also lists the computation times on a number of computers (ranging from supercomputers to personal computers). The results clearly illustrate the necessity of supercomputers for such time-consuming computations.