An exploration of a stochastic model of solute transport

Abstract

A model of groundwater solute transport is being developed by Don Kulasiri (Kulasiri, 1997). This is part of a larger project being undertaken by Lincoln Environmental. In the model, the velocity of the water in the porous media has a component which is dependent on piezometric head according to Darcy’s law, and a random component. The latter represents the variation which has been observed and which is assumed to be due to the porous media. The model also represents the diffusive process experienced by the solute in both a deterministic (Fick’s law) and random manner. Thus we have a model which comprises stochastic partial differential equations in 3 dimensions. The difficulty confronted by the model developer is how to get a good understanding of the behaviour of the model and thus have more confidence that it is working as expected. This short paper describes some attempts to visualise the behaviour of this model and shows how some inadequacies in its early implementation were discovered and a better understanding of the model’s behaviour was obtained.