document: Time-integration of multiphase chemistry in size-resolved cloud models 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
doc_bio_tags: O O B I O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O B I O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O
extractive_keyphrases: multiphase chemistry cloud drops chemical species chemical reactions multiphase chemical systems aqueous phase chemistry gas phase chemistry approximate matrix factorization operator splitting linear algebra sparse jacobians
abstractive_keyphrases: size-resolved cloud models time-integration schemes air pollution modelling