Positive advection schemes for environmental studies

The study of air- and water quality models in geophysical flow often give rise to advection-diffusion-reaction equations. The method of fractional steps makes it possible to separate these processes and to employ for each physical mechanism an efficient numerical technique. The advective part of the set of equations will be investigated. It is difficult to design an appropiate advection scheme. Moreover, when non-linear reactions are involved, it is in many cases necessary to incorporate the restriction that the numerical solution is nonnegative. This demand as well as practical conditions make it difficult to design a suitable numerical scheme. Presents a comparative study of a number of special numerical methods that approximate the solution of the advection equation with two spatial dimensions. To get a clear and coherent impression of the performance of the different advection schemes a consistent set of tests has been made. A number of objective criteria discriminate between the various results.