Numerical and Stochastic Modeling of Advection and Diffusion of Water Pollutants

摘要

To predict the dispersion of pollutants in shallow water in case of a calamity (such as a ship accident) one can adopt an Eulerian point of view and solve the well-known two-dimensional advection-diffusion equation numerically or one can use a stochastic Lagrangian particle model. The Lagrangian approach is mass conserving, while concentrations can never become negative. However, for long simulation periods many particles are required to obtain acceptable results. To combine the best of the two approaches the authors developed in this paper a particle model that is exactly consistent with the general advection-diffusion equation and use this stochastic model only to describe the spreading of the pollutant during the period short after the calamity. From a certain time, when the particles are spread over a large area the authors determine the concentration and solve the advection-diffusion equation numerically by means of an ADI/FEM-scheme.