IMPLEMENTATION AND PERFORMANCE OF THE TIME INTEGRATION OF A 3D NUMERICAL TRANSPORT MODEL

The total solution of a three-dimensional model for computing the tran sport of salinity, pollutants, suspended material (such as sediment or mud), etc. in shallow seas involves many aspects, each of which has t o be treated in an optimal way in order to cope with the tremendous co mputational task involved. In this paper we focus on one of these aspe cts, i.e. on the time integration, and discuss two numerical solution methods. The emphasis in this paper is on the performance of the metho ds when implemented on a vector/parallel, shared memory computer such as a Gray-type machine. The first method is an explicit time integrato r and can straightforwardly be vectorized and parallelized. Although a stabilizing technique has been applied to this method, it still suffe rs from a severe time step restriction. The second method is partly im plicit, resulting in much better stability characteristics; however, a s a consequence of the implicitness, it requires in each step the solu tion of a large number of tridiagonal systems. When implemented in a s tandard way, the recursive nature would prevent vectorization, resulti ng in a very long solution time. Following a suggestion of Golub and V an Loan, this part of the algorithm has been tuned for use on the Gray C98/4256. On the basis of a large-scale test problem, performance res ults will be presented for various implementations.