TIME INTEGRATION OF 3-DIMENSIONAL NUMERICAL TRANSPORT MODELS

We analyse three-dimensional models for computing transport of salinity, pollutants, suspended material (such as sediment or mud), etc. The main purpose of this paper is to present an overview of the various possibilities for the time discretization of the advection and diffusion terms that can take advantage of the parallelization and vectorization facilities offered by CRAY-type computers. Among the suitable time integration techniques, we have both explicit and implicit methods. In explicit methods, the parallelization is straightforward, but these methods are hampered by a severe time step restriction due to stability. This can be avoided by selecting an implicit method; however, such a choice necessitates the frequent solution of systems of equations. For the implicit methods considered in this survey, these systems essentially have a tradiagonal structure. Even for this relatively simple form, the greater part of the total solution time is spent in solving these systems. Therefore, this part of the algorithm needs special attention in order to get good performance on parallel/vector architectures. Following a suggestion of Golub and Van Loan, we have experimented with several implementations on a CRAY YMP4, which will be reported.