A Splitting Numerical Method for Primary and Secondary Pollutant Models

A splitting numerical method is proposed to study the effect of gravitational settling velocity and chemical reaction on pollutants emitted from a point source on the boundary of an urban area. The governing ultra-parabolic equation degenerates on the part of the boundary and we apply a fitted finite volume scheme in order to resolve the degeneration and to preserve the positivity property of the solution (concentration of the pollutant). Computational experiments illustrate the efficiency of our numerical method.