文档介绍：Mathematics puters in Simulation 61 (2003) 115–137
Stochastic Lagrangian models and algorithms for spatially
inhomogeneous Smoluchowski equation
Karl Sabelfeld a,b,∗, Anastasia Kolodko b
a Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany
b Institute putational Mathematics and Mathematical Geophysics, Russian Academy of Sciences,
Lavrentieva str. 6, 630090 Novosibirsk, Russia
Received 1 May 2002; accepted 6 June 2002
Abstract
The following generally unsolved yet problem is studied: construct the solution of a spatially inhomogeneous
Smoluchowski equation governing coagulating and diffusing particles in a host gas, on the basis of solutions to
homogeneous Smoluchowski equation. In [Math. Comput. Simul. 49 (1999) 57], we solved this problem in the
case when there is no diffusion. The non-zero diffusion term plicates the situation. Under some
general assumptions we give the interrelations between the homogeneous and inhomogeneous cases. This provides
an effective numerical scheme especially when the host gas is pressible. New Lagrangian scheme leads to a
new model governing by a Smoluchowski type equation with an additional effective source. We give a numerical
comparison of these two models.
puter time of the new algorithm is so dramatically decreased, compared to the conventional deterministic
algorithm (tens of hours drop down to several minutes) that many practical problems like the formation of soot
particles in flames or chemical reactions coupled to formation of a new phase can be solved in a reasonable
computer time. However, this method works only if the diffusion coefficient of all particles is the same which can
be a reasonable approximation only for special systems. The problem of generalisation of the method presented to
the case when the diffusion coefficient depends on the particle’s size is open.
© 2002 IMACS. Published by Elsevier Science . All rights reserved.
MSC: 65