The mathematical terms describing the chemical reactions introduce nonlinearity
in the systems of partial differential equations (PDEs), by which most of the
large-scale air pollution models are described. The numerical treatment of these nonlinear
terms causes normally great difficulties. Several algorithms for handling the
chemical part of a particular air pollution model, the Unified Danish Eulerian Model
(UNI-DEM), are described and discussed. The ideas used in the development of these
methods are rather general and can also be applied in connection with other air pollution
models as well as in the numerical treatment of some systems of PDEs that arise in
other areas of science and engineering.
Keywords: Chemical sub-models, Unified Danish Eulerian Model (UNI-DEM),
diffusivity coefficient, horizontal transport, horizontal diffusion, dry and wet
depositions, vertical transport, deposition coefficient, vertical exchange, Quasi-
Steady-State-Approximation (QSSA), ordinary differential equations (ODEs),
condensed Carbon Bond Mechanism (CBM IV), sulphur pollutants, nitrogen
pollutants, ozone, hydro-carbons, condition number, stiff ODE, A-stable, Strongly
A-stable, L-stable method.
