Bruno Sportisse, Anne Jaubertie and Pierre Plion |

Conference St Venant 97.

Numerous applications, such as air pollution modelling, require to take into account the coupling of chemical phenomena with fluid mechanics. The underlying models are particularly difficult to handle numerically, due to many reasons. First, one has often to consider a large number of chemical species and reactions in order to have a fine description of the chemistry. This increases the computational cost, which mainly depends on the power three of the number of species. Second, the wide range covered by the characteristic time scales of chemical phenomena implies the stiffness of the resulting equations. This motives the classical use of specific solvers for the time integration (Sandu \& al 1996, Jay \& al 1997). At last, there is a strong sensitivity in many physical parameters that are difficult to measure (especially initial conditions and rate coefficients). Using fast and robust algorithms for the chemical part is therefore a challenging point, its integration consuming until 90\% of the CPU time. Chemists have used for a long time procedures in order to handle these difficulties. Lumping strategies (Hesstvedt \& al 1978) consist in grouping species, whose individual evolution is unimportant, in order to {\it reduce} the dimension of the system. Reducing strategies are based on considerations about the lifetimes of species and reactions: the stiffness is linked with a two-time scales behaviour and the reducing procedure yields getting ride of the fast dynamics. Some computational approaches (Lam \& al 1991, Maas \& al 1992) have been recently proposed: they are mainly equivalent with the search for a dominant invariant subspace of the jacobian matrix. One can wonder if these methods are not double-edged for systems issued specifically from chemical kinetics: they apply general results (which legitimates their validity) but they forget the underlying ``chemical origin'' of the stiffness. The counterpart is then probably an increasing cost of algebraic manipulations (due to the precise study of the jacobian) and surely a loss of physical understanding. These remarks justify our interest in conventional methods. Our aim is to present briefly the physical and mathematical backgrounds. We mention thereafter some results justifying the proposed algorithm (second section). We present in the last section some applications we currently investigate in air pollution modelling.