Computational challenges in the numerical treatment of large air pollution models

Abstract

Air pollution, especially the reduction of the air pollution to some acceptable levels, is an important environmental problem, which will become even more important in the next 10–20 years. This problem can successfully be studied when high-resolution comprehensive models are developed and used on a routine basis. However, such models are very time-consuming, even when modern high-speed computers are available. Indeed, if an air pollution model is to be applied on a large space domain by using fine grids, then its discretization will always lead to huge computational problems. Assume, for example, that the space domain is discretized by using a (480 × 480) grid and that the number of chemical species studied by the model is 35. Then several systems of ordinary differential equations containing 8 064 000 equations have to be treated at every time-step (the number of time-steps being typically several thousand). If a three-dimensional version of the same air pollution model is to be used, then the figure above must be multiplied by the number of layers. It is extremely difficult to treat such large computational problems, even when the fastest computers that are available at present are used. There is an additional great difficulty, which is very often underestimated (or even neglected) when large application packages are moved from sequential computers to modern parallel machines. The high-speed computers have normally a very complicated memory architecture and, therefore, the task of producing an efficient code for the particular high-speed computer that is available is both extremely hard and time consuming. The use of standard parallelization tools in the solution of the problems sketched above is discussed in this paper. Numerical results obtained on different types of parallel computers are presented.