SPLITTING METHODS FOR 3-DIMENSIONAL BIO-CHEMICAL TRANSPORT

Splitting methods for the time integration of three-dimensional transp ort-chemistry models offer interesting prospects: second-order accurac y can be combined with sufficient stability, and the amount of implici tness can be reduced to a manageable level. Furthermore, exploiting th e parallelization and vectorization features of the algorithm, a reali stic simulation with many species over long time intervals becomes fea sible. As an alternative to the usual splitting functions, such as co- ordinate splitting or operator splitting, we discuss in this paper a s plitting function that is of hopscotch type. Both for a second-order, symmetric spatial discretization (resulting in a three-point coupling in each direction), and for a third-order, upwind discretization (givi ng rise to a five-point coupling, in general), we define a particular variant of this hopscotch splitting. These splitting functions will be combined with an appropriate splitting formula, resulting in second-o rder (in time) splitting methods. A common feature of both hopscotch s plitting functions is that we have only coupling in the vertical direc tion, resulting in a stability behaviour that is independent of the ve rtical mesh size; this is an important property for transport in shall ow water. Another characteristic of this hopscotch-type splitting is : hat it allows for an easy application of domain decomposition techniqu es in the horizontal directions. Two choices for the splitting formula will be presented. The resulting methods have been applied to a large -scale test problem and the numerical results will be discussed. Furth ermore, we show performance results obtained on a Gray C98/4256. As pa rt of the project TRUST (Transport and Reactions Unified by Splitting Techniques), preliminary versions of the schemes are available for ben chmarking.