Physically-based modeling and simulation

The thesis deals with the modeling of air pollution transportation and dispersion processes in the atmosphere, more precisely with the numerical approaches to solve such models. The modeling of air pollution has a great importance for prediction of the contaminations and it helps with understanding of the process and with elimination of its consequences. The models which are described by partial differential equations, namely advection-diffusion equations, and thus they can be solved by numerous analytical/numerical methods are in the scope of the thesis. In particular, well known method of lines (MoL) and several models based on it together with the possibility to accelerate the computation are studied in the first half of the work. It is shown that MoL approach is still suitable for many concrete models and it has a great potential for parallelization on graphics cards. Quite young ELLAM method and its application to solve atmospheric advection-diffusion equations is the second objective. A concrete form of ELLAM method and its proposed adaptation approaches are evaluated and it is shown that it overcomes the current state of the art methods in many cases.