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The moment‐guided Monte Carlo method
Author(s) -
Degond Pierre,
Dimarco Giacomo,
Pareschi Lorenzo
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2345
Subject(s) - moment (physics) , monte carlo method , statistical physics , non equilibrium thermodynamics , kinetic monte carlo , work (physics) , particle (ecology) , set (abstract data type) , mathematics , physics , computer science , classical mechanics , thermodynamics , statistics , oceanography , programming language , geology
In this work we propose a new approach for the numerical simulation of kinetic equations through Monte Carlo schemes. We introduce a new technique that permits to reduce the variance of particle methods through a matching with a set of suitable macroscopic moment equations. In order to guarantee that the moment equations provide the correct solutions, they are coupled to the kinetic equation through a nonequilibrium term. The basic idea, on which the method relies, consists in guiding the particle positions and velocities through moment equations so that the concurrent solution of the moment and kinetic models furnishes the same macroscopic quantities. Copyright © 2010 John Wiley & Sons, Ltd.