Cited by 398Gas Dynamics and Kinetic TheoryAdvanced Physical and Chemical Molecular InteractionsLattice Boltzmann Simulation Studies

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Direct Simulation Scheme Derived from the Boltzmann Equation. I. Monocomponent Gases

Nanbu, Kenichi·1980·Journal of the Physical Society of Japan

DOI 10.1143/jpsj.49.2042

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Abstract

The stochastic law that prescribes the velocities of simulated molecules after a small time increment was derived from the Boltzmann equation. The scheme to determine the velocity of a molecule after a small time increment is divided into three steps. The first step gives the collision probability of the molecule without specifying its collision partner. The second step gives a conditional probability distribution. If the molecule is accepted in the first step as a colliding molecule, its collision partner is sampled from this probability distribution. The last step gives a probability density from which the direction of the relative velocity after collision is sampled, and hence the step gives the post-collision velocity of the molecule. It is shown that the use of the present simulation scheme gives an exact solution of the Boltzmann equation.

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Authors: Nanbu, K.
Affiliations: Tohoku University (JP)
Corresponding author: Nanbu, Kenichi
Venue: Journal of the Physical Society of Japan
Publisher: Physical Society of Japan
Published: 1980-11-15
Volume: 49
Issue: 5
Pages: 2042-2049
ISSN: 0031-9015 (ISSN-L)
1347-4073
DOI: 10.1143/jpsj.49.2042
OpenAlex: W1981163355
Cited by: 397
References: 6
Citations by year: 2026: 7 · 2025: 15 · 2024: 9 · 2023: 17 · 2022: 22 · 2021: 12 · 2020: 10 · 2019: 10 · 2018: 4 · 2017: 13 · 2016: 23 · 2015: 8 · 2014: 11 · 2013: 10 · 2012: 8
FWCI: 11.65
Type: journal article
Language: en
Open access: closed
Locations: Journal of the Physical Society of Japan (publishedVersion)
Topics: Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
Physical Sciences › Engineering › Computational Mechanics › Lattice Boltzmann Simulation Studies
Keywords: direct simulation, Boltzmann equation, collision probability, conditional distributions, rarefied gas dynamics

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Direct Simulation Scheme Derived from the Boltzmann Equation. I. Monocomponent Gases

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