A stochastic method for solving Smoluchowski's coagulation equation
Authors
- Kolodko, Anastasya
- Sabelfeld, Karl
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 65C05 76F99
Keywords
- coagulation equation, Monte Carlo estimators, spatially inhomogeneous case, isotropic turbulent flow
DOI
Abstract
This paper studies a stochastic particle method for the numerical treatment of Smoluchowski equation governing the coagulation of particles in a host gas. Convergence in probability is established for the Monte Carlo estimators, when the number of particles tends to infinity. The deterministic limit is characterized as the solution of a discrete in time version of the Smoluchowski equation. Under some restrictions it is shown that this stochastic finite difference scheme is convergent to the solution of the original Smoluchowski equation. Extensions on a nonhomogeneous Smoluchowski equation are given, and in particular, a coagulation process in an isotropic fully developed turbulent flow is studied.
Appeared in
- Math. Comput. Simulation 49(1-2) (1999), pp. 57-79
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