An hybrid method for the Boltzmann equation

Russel E. Caflisch, Giacomo Dimarco, Lorenzo Pareschi

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this work, we discuss the generalization of the hybrid Monte Carlo schemes proposed in [1, 2] to the challenging case of the Boltzmann equation. The proposed schemes are designed in such a way that the number of particles used to describe the solution decreases when the solution approaches the equilibrium state and consequently the statistical error decreases as the system approaches this limit. Moreover, as opposite to standard Monte Carlo methods which computational cost increases with the number of collisions, here the time step and thus also the computational cost is independent from the collisional scale. Thanks to the local coupling of Monte Carlo techniques for the solution of the Boltzmann equation with macroscopic numerical methods for the compressible Euler equations, the scheme degenerates to a finite volume scheme for the compressible Euler equations in the limit of an infinite number of collisions without introducing any artificial transition. A simple applications to one-dimensional Boltzmann equation is presented to show the performance of the new method.

Original languageEnglish (US)
Title of host publication30th International Symposium on Rarefied Gas Dynamics, RGD 2016
EditorsHenning Struchtrup, Andrew Ketsdever
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735414488
StatePublished - Nov 15 2016
Event30th International Symposium on Rarefied Gas Dynamics, RGD 2016 - Victoria, Canada
Duration: Jul 10 2016Jul 15 2016

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


Other30th International Symposium on Rarefied Gas Dynamics, RGD 2016

ASJC Scopus subject areas

  • General Physics and Astronomy


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