An Efficient Stochastic Algorithm for Studying Coagulation Dynamics and Gelation Phenomena

Abstract

A new class of efficient stochastic algorithms for the numerical treatment of coagulation processes is proposed. The algorithms are based on the introduction of fictitious jumps combined with an acceptance-rejection technique for distributions depending on particle size. The increased efficiency is demonstrated by numerical experiments. In particular, gelation phenomena are studied.

Numerical simulations of soot aggregation in premixed laminar flames

“…The efficiency of the algorithm has been vastly improved by use of a time-splitting technique for the fast surface growth processes, and by introducing a majorant kernel [10,5] for the coagulation term. Another important feature of the new code is the ability to handle essentially an infinite number of internal coordinates, thereby tracking the positions and radii of every primary particle of the aggregate structure.…”

Convergence of a finite volume scheme for coagulation-fragmentation equations

“…But occurrence of gelation depends on the behaviour of kernels a and b for large values of the volume variable x. On the other hand, discretizing these terms makes it necessary to truncate the infinite integrals in formulae (5)- (6). But this means restricting the domain of action of kernels a and b to a bounded set of volumes x, that is, preventing coagulation to occur among particles with volume exceeding a fixed value.…”

“…We refer for instance to [7,18] for deterministic methods, [2,6,13] for stochastic methods, and the references therein. However, there are few results concerning the convergence analysis of numerical methods for coagulation and fragmentation models (see [17] for quasi Monte-Carlo methods).…”

A Majorant Kernel-Based Monte Carlo Method for Particle Population Balance Modeling

“…This note proposes a novel scheme for quickly computing the maximum coagulation rate, namely through the use of majorant kernel. The concept of majorant kernel was initially proposed by (Eibeck and Wagner, 2000) and (Goodson and Kraft, 2002) to improve the efficiency of the numerical treatment of the coagulation problems. In particular, they designed a Monte Carlo algorithm using fictitious jumps and majorant kernel (in place of the original kernel) to simulate particle coagulation.…”