TIME INTEGRATION OF 3-DIMENSIONAL NUMERICAL TRANSPORT MODELS

We analyse three-dimensional models for computing transport of salinit y, pollutants, suspended material (such as sediment or mud), etc. The main purpose of this paper is to present an overview of the various po ssibilities for the time discretization of the advection and diffusion terms that can take advantage of the parallelization and vectorizatio n facilities offered by CRAY-type computers. Among the suitable time i ntegration techniques, we have both explicit and implicit methods. In explicit methods, the parallelization is straightforward, but these me thods 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 essenti ally have a tradiagonal structure. Even for this relatively simple for m, the greater part of the total solution time is spent in solving the se systems. Therefore, this part of the algorithm needs special attent ion in order to get good performance on parallel/vector architectures. Following a suggestion of Golub and Van Loan, we have experimented wi th several implementations on a CRAY YMP4, which will be reported.