Unstructured Adaptive Mesh MOL Solvers for Atmospheric Reacting Flow Problems

In this chapter the method of lines is applied to computational models of reacting flow arising from atmospheric applications. These computational models describe the chemical transformations and transport of species in the troposphere and have an essential role in understanding the complex processes which lead to the formation of pollutants such as greenhouse gases, acid rain and photochemical oxidants. In order to make good comparisons with the limited experimental data available it is important to have a high degree of computational resolution, but at the same time to model emissions from many different sources and over large physical domains. This chapter is thus concerned with how to achieve this by using the method of lines combined with spatial mesh adaptation techniques. Achieving high resolution in air pollution models is a difficult challenge because of the large number of species present in the atmosphere. The number of chemical rate equations which need to be solved rises with the number of species, and for high resolution 3-dimensional calculations, detailed chemical schemes can become prohibitively large. The range of reaction time-scales often leads to stiff systems of differential equations which require more expensive implicit numerical solvers. Previous work has shown (Talat, [31], Tomlin et al., [32, 33, 12] Hart et al.,[13]) that coarse horizontal resolution can have the effect of increasing horizontal diffusion to values many times greater than that described by models, resulting in the smearing of pollutant profiles and an underestimation of maximum concentration levels. A review paper by Peters et al. [22] highlights the importance of developing more efficient grid systems for the next generation of air pollution models in order to “capture important smaller scale atmospheric phenomena”. In general the effects of mesh resolution have been well noted by the atmospheric modelling community and attempts have been made to improve mesh resolution at the same time as trying to avoid excessive extra computational work. The usual approach is to use nested or telescopic grids, where the mesh is refined in certain regions of the horizontal domain which are considered of interest (Jacobs et al., [15], Rajaona et al.,[24], Sunderam et al., [30], Sillman et al.,[26]). This may include for example regions of high emissions such as urban areas, or close to regions where significant monitoring is taking place. Previous work has shown however (Tomlin et al.[32]) that such telescopic grids often cannot resolve plume structures occurring outside of the nested regions and that adaptive refinement in the horizontal domain can provide higher accuracy without entailing large extra computational costs. The primary reason is that away from