The linear process deferment algorithm: A new technique for solving population balance equations

In this paper a new stochastic algorithm for the solution of population balance equations is presented. The population balance equations have the form of extended Smoluchowski equations which include linear and source terms. The new algorithm, called the linear process deferment algorithm (LPDA), is used for solving a detailed model describing the formation of soot in premixed laminar flames. A measure theoretic formulation of a stochastic jump process is developed and the corresponding generator presented. The numerical properties of the algorithm are studied in detail and compared to the direct simulation algorithm and various splitting techniques. LPDA is designed for all kinds of population balance problems where nonlinear processes cannot be neglected but are dominated in rate by linear ones. In those cases the LPDA is seen to reduce run times for a population balance simulation by a factor of up to 1000 with a negligible loss of accuracy.