The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality. On an other...

The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality. On an other...