Advection and diffusion are fundamental processes in the atmosphere. They express the permanent balance between inertial and viscous forces. Some numerical treatments the equations, describing these processes, are presented. Three spatial discretization techniques, second order finite differences, linear finite element and pseudospectral, are tested in connection with a finite difference time integration. Dissipation, dispersion and stability of the numerical schemes for the linearized equations are investigated both theoretically and with the help of numerical simulations. Results with non-linear equations are also shown.

In conclusion there is a presentation of the less conventional Monte Carlo method for diffusion.