In realistic air-pollution models a variety of physical and chemical processes have to be taken Into consideration. The most important processes for constituents are advection and (turbulent) diffusion in the atmosphere, emission from diffuse and concentrated sources, wet and dry deposition and (photo- )chemical interactions. A mass balance, that reflects these processes is difficult to solve directly with numerical mathematical methods. However, the method of fractional steps (Yanenko, 1971) makes it possible to treat the different processes separately. Thus an algorithm that is most suitable for the approximation of a particular sub-process, such as advection, can be chosen.
Photo-chemical interactions play a substantial role in air-pollution situations. They are described by non-linear mathematical equations, which in many cases demand for their numerical solution that the chemical constituent concentrations remain non-negative. It turns out to be especially hard to construct numerical advection schemes that are non-negative as well as mass conserving and accurate enough. Therefore the larger part of this study is devoted to a comparative study of a number of spectal numerical methods that approximate the solution of the advection equations with two spatial dimensions. The best methods that came out of previous comparison studies have been chosen, together with some methods which appeared in recent literature.
To get a clear and coherent Impression of the performance of these advection schemes a consistent set of tests has been made on a VAX 11/750 under the UNIX 4.1 system. A number of objective criteria discriminate between the various outcomes. Also practical results such as computer time consumption and storage requirements are given. The results indicate that the Second Moment Method Is a robust and relatively cheap method for the resolution of the advection equation, although its storage requirements can be prohibitive. For a more detailed discussion see section 2.11.
Numerical methods for the treatment of the vertical structure and the non-linear chemical Interactions are not Included in this report. These will be the subject of a subsequent investigation.
Th. L.van Stijn, J.van Eijkeren and N. Praagman. A comparison of numerical methods for air-quality models
KNMI number: WR-87-06, Year: 1987, Pages: 100