A finite volume difference scheme for a model of settling particle dispersion from an elevated source in an open-channel flow

A finite volume fitted difference scheme is constructed to solve the unsteady convective-diffusion equation transformed on a finite domain, modeling longitudinal dispersion of suspended particles with settling velocity in a turbulent shear flow over a rough-bed surface. First we discuss the well-posedness of the differential problem and the non-negativity of its solution. Then, to overcome the degeneracy at the part of the boundary, starting from the divergent form of the equation we perform a local fitted space discretization. This approximation is determined by a set of two-point boundary value problems. Non-negativity of the numerical concentration of suspended fine particles is proved. Some results from computational experiments are presented to illustrate the properties of the constructed scheme.