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M. Ebner, S. Winkler:
"Comparison of Finite Difference Method and Random Walk Method in ARGESIM Benchmark C19 'Pollution and Groundwater Flow'";
Simulation Notes Europe, 24 (2014), 1; 51 - 54.

Groundwater represents one of the most important sources so as to satisfy the steadily increasing demand of pure water in modern times. However, groundwater is very susceptible to many kinds of pollution whose causes can usually be divided into one of two categories: point-source and nonpoint-source pollution. In this comparison a particular focus was put on the modelling of a 2D-homogeneous groundwater body and the contamination of its groundwater stream caused by a steady point-source pollution in case of a uniform pore-water velocity. Three different tasks were regarded: in task A, the pollution propagation was investigated and compared to an approximated analytical solution in case of a permanent activation and when the pollution reduction works according to a set schedule instead. In total, two differenct computational approaches were chosen and implemented in Matlab whereby one cosisted of a finite difference method and the other was based on a random walk ansatz. Similar results were obtained but further parameter studies could be helpful.

http://dx.doi.org/10.11128/sne.24.bn19.102235

http://publik.tuwien.ac.at/files/publik_253888.pdf