Numerical integration of chemical ODE problems arising in air pollution models

The numerical treatment of a regional air pollution model (such models are, as a rule, described mathematically by systems of partial differential equations) leads to the solution of very large computational problems. The chemical sub‐model of an air pollution model is normally the most time‐consuming part of the computational work. The application of appropriate discretization and splitting procedures reduces the chemical sub‐model to a large number of relatively small ODE systems (one such system per grid‐point). In the process of searching for efficient numerical algorithms for the chemical sub‐models one can carry out experiments by using only one such ODE system in order to facilitate the work. This approach has been used in connection with a particular chemical scheme, the condensed CBM IV scheme, which is used in several large air pollution models. Six integration algorithms have been tested on a set of typical scenarios (consisting of different starting concentrations and/or of different values of the emissions). The advantages and the disadvantages of the algorithms tested are discussed. The final decision about the most efficient algorithm, among the algorithms tested, should be made after a second series of experiments. The coupling of the chemical process with the transport of air pollution (on, at least, a two‐dimensional domain) together with the application of high‐speed computers has to be studied in the second series of experiments, which will be performed in a subsequent paper.