Time-integration of multiphase chemistry in size-resolved cloud models Original Research Article

The existence of cloud drops leads to a transfer of chemical species between the gas and aqueous phases. Species concentrations in both phases are modified by chemical reactions and by this phase transfer. The model equations resulting from such multiphase chemical systems are nonlinear, highly coupled and extremely stiff. In the paper we investigate several numerical approaches for treating such processes. The droplets are subdivided into several classes. This decomposition of the droplet spectrum into classes is based on their droplet size and the amount of scavenged material inside the drops, respectively. The very fast dissociations in the aqueous phase chemistry are treated as forward and backward reactions. The aqueous phase and gas phase chemistry, the mass transfer between the different droplet classes among themselves and with the gas phase are integrated in an implicit and coupled manner by the second order BDF method. For this part we apply a modification of the code LSODE with special linear system solvers. These direct sparse techniques exploit the special block structure of the corresponding Jacobian. Furthermore we investigate an approximate matrix factorization which is related to operator splitting at the linear algebra level. The sparse Jacobians are generated explicitly and stored in a sparse form. The efficiency and accuracy of our time–integration schemes is discussed for four multiphase chemistry systems of different complexity and for a different number of droplet classes.