On two numerical schemes of the Monte Carlo method for solving the Boltzmann equation

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On two numerical schemes of the Monte Carlo method for solving the Boltzmann equation. / Moskaleva, N. M.

In: Vestnik St. Petersburg University: Mathematics, Vol. 43, No. 4, 12.2010, p. 256-262.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{71420cbf0212471f93f046a24ad43de6,

title = "On two numerical schemes of the Monte Carlo method for solving the Boltzmann equation",

abstract = "Two numerical schemes of the Monte Carlo method for solving the Cauchy problem for the Boltzmann equation are constructed and tested. They are based on a well-known relationship between a nonlinear integral equation and a random process. Procedures for modeling special random processes on whose trajectories unbiased estimators for the solution are described. Each scheme has its own domain of applicability, in which its advantages manifest themselves. The conjugate scheme is convenient for calculating the Boltzmann distribution function at high velocities (on {"}tails{"}). For the example of the BKW solution, the applicability of the schemes is numerically analyzed.",

keywords = "{"}conjugate scheme{"}, {"}direct{"} scheme, majorant condition, the Boltzmann equation, the Monte-Carlo Method, the Neumann series, trajectory of a molecule",

author = "Moskaleva, {N. M.}",

note = "Funding Information: ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 08 01 00194.",

year = "2010",

month = dec,

doi = "10.3103/S1063454110040102",

language = "English",

volume = "43",

pages = "256--262",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - On two numerical schemes of the Monte Carlo method for solving the Boltzmann equation

AU - Moskaleva, N. M.

N1 - Funding Information: ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 08 01 00194.

PY - 2010/12

Y1 - 2010/12

N2 - Two numerical schemes of the Monte Carlo method for solving the Cauchy problem for the Boltzmann equation are constructed and tested. They are based on a well-known relationship between a nonlinear integral equation and a random process. Procedures for modeling special random processes on whose trajectories unbiased estimators for the solution are described. Each scheme has its own domain of applicability, in which its advantages manifest themselves. The conjugate scheme is convenient for calculating the Boltzmann distribution function at high velocities (on "tails"). For the example of the BKW solution, the applicability of the schemes is numerically analyzed.

AB - Two numerical schemes of the Monte Carlo method for solving the Cauchy problem for the Boltzmann equation are constructed and tested. They are based on a well-known relationship between a nonlinear integral equation and a random process. Procedures for modeling special random processes on whose trajectories unbiased estimators for the solution are described. Each scheme has its own domain of applicability, in which its advantages manifest themselves. The conjugate scheme is convenient for calculating the Boltzmann distribution function at high velocities (on "tails"). For the example of the BKW solution, the applicability of the schemes is numerically analyzed.

KW - "conjugate scheme"

KW - "direct" scheme

KW - majorant condition

KW - the Boltzmann equation

KW - the Monte-Carlo Method

KW - the Neumann series

KW - trajectory of a molecule

UR - http://www.scopus.com/inward/record.url?scp=84859728357&partnerID=8YFLogxK

U2 - 10.3103/S1063454110040102

DO - 10.3103/S1063454110040102

M3 - Article

AN - SCOPUS:84859728357

VL - 43

SP - 256

EP - 262

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 86643348