Wilson Charles: Application of stochastic differential equations to model dispersion of pollutants in shallow water

A two dimensional stochastic differential equations(SDEs) to describe the dispersion of pollutants in shallow water is developed. By deriving the Kolmogorov's forward partial differential equation or commonly called Fokker-Planck equation, the SDEs model is shown to be consistent with the two-dimensional advection-diffusion equation. To improve the behaviour of the model shortly after the deployment of the pollutant, the SDEs called random flight model is developed too. It is shown that over long simulation periods, this model is again consistent with the advection diffusion equation. The simulated results in an ideal two dimensional domain are presented to predict the dispersion of a pollutant in the shallow waters.

References.

1.    Adaptive stochastic numerical scheme in parallel random walk models for transport problems in shallow water,
W.M. Charles, E. van den Berg, H.X. Lin, A.W. Heemink,Mathematical and Computer Modelling, 50(7--8), 2009, 1177--1187.

2.     Coloured noise for dispersion of contaminants in shallow waters
       W.M. Charles, A.W. Heemink, E. van den Berg, Journal of Applied Mathematical Modelling, 33(2), 2009, 1158--1172.

3.     Parallel and distributed simulation of sediment dynamics of shallow waters using particle decomposition approach
W.M. Charles, E. van den Berg, H.X. Lin, A.W. Heemink. M. Verlaan, Journal of Parallel and Distributed Computing, 68(6), 2008, 717--728.


4.    Variable time stepping in parallel particle models for transport problems in shallow waters
W.M. Charles, E. van den Berg, H.X. Lin, A.W. Heemink,
Proceedings of the 8th International Conference on Modelling, Monitoring and Management of Water Pollution, Bologna, Italy, 2006.

5.    Stochastic particle models for transport problems in coastal waters
W.M. Charles, A.W. Heemink, E. van den Berg, Proceedings of the 29th International Conference on Coastal Engineering, Lisbon, Portugal, 2005, 69--79.

6.    Stochastic modelling of dispersion in shallow water
A.    W. Heemlnk,  Journal of Stochastic Hydrol. Hydraul. 4 (1990) 161-174