Lin, Cosman, Heemink, Stijnen, van Beek: Parallelization of the Particle Model SIMPAR

Particle methods are an important technique for simulating transport phenomena such as the transport of pollutants in coastal waters. Particle methods can quite accurately predict the pollutant transport in cases of steep concentration gradients after the pollutant has just entered into the water, whereas conventional numerical methods such as finite difference and finite volume methods may have difficulties. Since the computation time in a particle model increases linearly with the number of particles, this often forms a limiting factor. We consider the parallelization of the particle model SIMPAR. Different load balancing and communication optimization possibilities are investigated. Some experiments with the parallel implementation of the SIMPAR model on a cluster of workstations and the Cray T3E are also reported. Introduction Particle methods are an important technique for simulating transport phenomena such as the transport of pollutants in coastal waters. These methods are especially useful when the concentration gradient is very steep. For example at the time right after an accident when the pollutant gets into the water, there is a steep concentration concentration pattern (see e.g. [4]). In such cases conventional numerical methods such as finite difference and finite volume methods may have difficulties dealing with the almost delta-like gradient. Particle methods can predict the pollutant transport in these situations quite accurately. By interpreting the advection-diffusion equation as a Fokker-Planck equation, one can derive a stochastic Lagrangian particle model for the particle positions (which represent the pollutant). A particle model is briefly described below. Consider a shallow sea with a depth h(x,y,t) and (horizontal) water velocities u(x,y,t) and v(x,y,t) along the xand y-directions respectively. The continuity equation states that the flow velocities and the water depth h satisfies file:///D|/user/Lehfeldt/ICHE/1998-Cottbus/Document/Numerics.Det.165.paper.html (1 von 12) [20.11.02 08:45:25] Lin, Cosman, Heemink, Stijnen, van Beek: Parallelization of the Particle Model SIMPAR (1) They are usually determined by an (Eulerian) numerical hydrodynamic model. In our case, the simulation program TRIWAQ is used for calculating this deterministic background flow field prior to the start of the particle simulation. The dispersion process in shallow sea can be modelled using the following Ito stochastic differential equation ([1]):