Finite volume method solution of pollutant transport in catchment sheet flow

A finite volume numerical method was employed in the solution of two-dimensional pollutant transport in catchment sheet flow. The full dynamic wave constituted the sheet flow while the advection–diffusion equation with sink/source terms was the pollutant transport model. It is assumed that the solute in the surface active layer is uniformly distributed and the exchange rate of the solute between the active layer and overland flow are proportional to the difference between the concentrations in soil and water volume. Decrease of the solute transfer rate in the active surface layer caused by the transfer of solutes from soil to the overlying runoff is assumed to follow an exponential law. The equations governing sheet flow and pollutant transport are discretized using the finite volume method in space and an implicit backward difference scheme in time. The model was subjected to several numerical tests involving varying microtopographic surface, roughness, and infiltration. The results revealed that spatially varying microtopography plays an important role unlike the roughness and infiltration with respect to the total pollutant rate from the outlet of a catchment.