Zlatev Z., Dimov I. Computational and numerical challenges in environmental modelling

Elsevier, Amsterdam, London, New York, 2006, 393 pp. - ISBN-13: 978-0-444-52209-2
Reliable and robust control strategies for keeping the pollution caused by harmful chemical compounds below certain safe levels have to be developed and used in a routine way. Large mathematical models, in which all of the important physical and chemical processes are adequately described, can successfully be used to support this task. However, the use of large-scale mathematical models in which all of the important physical and chemical processes are adequately described leads, after the application of appropriate discretization and splitting procedures, to the treatment of huge computational tasks. In a typical simulation one has to perform several hundred runs. In each of these runs one has to carry out several thousand time-steps and at each time-step one has to solve numerically systems of coupled ordinary differential equations containing up to several million equations. Therefore, it is difficult to treat such large mathematical models numerically even when fast modern computers are available. Combined research by specialists from the fields of environmental and ecological modelling, numerical analysis, and scientific computing must be carried out in an attempt to resolve successfully the challenging computational problems that appear when comprehensive environmental studies are to be carried out.PDE systems arising in air pollution modelling and justification of the need for high speed computers
Using splitting techniques in the treatment of air pollution models
Treatment of the advection-diffusion phenomena
Treatment of the chemical part: general ideas and major numerical methods
Error analysis of the partitioning procedures
Efficient organization of the matrix computations
Parallel computations
Studying high pollution levels 233
Impact of future climate changes on high pollution levels
Implementation of variational data assimilation
Discussion of some open questions
AppendixSymbol Table. Author Index. Subject Index