Partitioning techniques and lumping computations for reducing chemical kinetics: APLA, an Automatic Partitioning and Lumping Algorithm

Rafik Djouad and Bruno Sportisse

Accepted for publication Applied Numerical Mathematics

The time integration of Air Pollution Models is a difficult task due to numerical stiffness, nonlinearity and coupling between equations and implicit schemes are usually advocated. Based on the slow/fast behaviour of the chemical dynamics , reducing procedures are alternative efficient techniques leading to non-stiff systems. Reduced models are defined by a set of {\it lumped species} and {\it algebraic constraints} and their validity is related with the correct partitioning of dynamics (species and reactions). By using some axiomatic hypothesis and algebraic properties we propose in this paper an efficient partitioning technique and an algorithm in order to compute the lumping of species in an automatic way. This is applied to four atmospheric chemical mechanisms.