Regularization and modeling of the Boltzmann collisional operator: Tcheremissine and Shakhov approaches

Oleg A. Rogozin, Vladimir V. Aristov, Aoping Peng, Zhihui Li

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    Solution of the Boltzmann equation involves many difficulties mainly associated with the nonlinear and nonlocal multidimensional nature of the collision term. To overcome them, two different strategies are commonly used: 1) highly efficient numerical algorithms and 2) simplified collision operators capable of reproducing the desired properties of the Boltzmann dynamics. In this work, two corresponding approaches proposed many years ago are considered and compared for some numerical examples. The Tcheremissine regularization method provides a flexible framework for designing conservative discrete-velocity methods. The Shakhov relaxation model is able to mimic the viscosity and thermal conductivity preserving the computational simplicity. The obtained results are in very good agreement, but, due to uncontrollable inaccuracy of relaxation models, some subtle discrepancies arise in regions where the velocity distribution function is far from equilibrium.

    Original languageEnglish
    Title of host publication31st International Symposium on Rarefied Gas Dynamics, RGD 2018
    EditorsDuncan Lockerby, David R. Emerson, Lei Wu, Yonghao Zhang
    PublisherAmerican Institute of Physics Inc.
    ISBN (Electronic)9780735418745
    DOIs
    Publication statusPublished - 5 Aug 2019
    Event31st International Symposium on Rarefied Gas Dynamics, RGD 2018 - Glasgow, United Kingdom
    Duration: 23 Jul 201827 Jul 2018

    Publication series

    NameAIP Conference Proceedings
    Volume2132
    ISSN (Print)0094-243X
    ISSN (Electronic)1551-7616

    Conference

    Conference31st International Symposium on Rarefied Gas Dynamics, RGD 2018
    Country/TerritoryUnited Kingdom
    CityGlasgow
    Period23/07/1827/07/18

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