Method of Lines versus Operator Splitting for reaction–diffusiuon systems with fast chemistryq

Operator Splitting methods are widely used for the numerical computation of reactive flows. The classical analysis of the error induced by such techniques is based on asymptotic expansions with respect to the splitting timestep Dt (supposed to be a small parameter). Such an assumption is unfortunately rather difficult to meet in real computations since Dt is actually much larger than the smallest physical timescales (defined by fast chemical phenomena). The usual error analysis has then to be replaced by another approach, which is associated with the multi-scale behaviour of the coupled system. We give here some theoretical indications and illustrate them with a monodimensional application in Air Pollution Modelling