No abstract

No abstract

No abstract

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.1. Introduction. The study of population balance problems for collections of particles that interact with each other via collisions has a long history-Bird [3] used this approach for gas dynamics in the 1970s. More recent applications include atmospheric aerosols (see, e.g., [4] and the references given there) and particle synthesis in flames [17].In these later cases interactions between the particles and the surrounding gas which operate linearly on the particle population have to be considered in addition to particle-particle interactions which have nonlinear effects. Work by some of the authors of this present paper on the formation of soot in laminar premixed flames [2,14] showed that a large amount of computer time was being devoted to the linear processes of particle-gas interactions.The purpose of this paper is to present a new algorithm that we call the linear process deferment algorithm (LPDA) and which reduces the time required for simulations. We also compare this new method to the general numerical analysis technique of splitting. LPDA is applicable to population models of systems other than soot where nonlinear processes are important but dominated in rate by linear ones.In this paper we first set out the population balance problem for soot formation and growth that we seek to solve. Then we give the structure of our original simulation procedures, the direct simulation algorithm (DSA). Detailed measurements of the

No abstract