Adequate numerical solution of air pollution problems by positive difference schemes on unbounded domains

In this work we deal with the numerical solution of some problems of air pollution. Since the problems are posed on unbounded domains we have to introduce artificial boundaries to confine the computational region. We construct and analyse (discrete) transparent boundary conditions for an implicit difference scheme. We discuss the concepts of positivity and monotonicity of difference schemes and briefly consider these properties of difference schemes for advection-diffusion equations arising in problems of air (and water) pollution. The efficiency and accuracy of our method is illustrated by an example.