Volume 18, Issue 3
Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation

Manuel Torrilhon

Commun. Comput. Phys., 18 (2015), pp. 529-557.

Published online: 2018-04

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  • Abstract

The accuracy of moment equations as approximations of kinetic gas theory is studied for four different boundary value problems. The kinetic setting is given by the BGK equation linearized around a globally constant Maxwellian using one space dimension and a three-dimensional velocity space. The boundary value problems include Couette and Poiseuille flow as well as heat conduction between walls and heat conduction based on a locally varying heating source. The polynomial expansion of the distribution function allows for different moment theories of which two popular families are investigated in detail. Furthermore, optimal approximations for a given number of variables are studied empirically. The paper focuses on approximations with relatively low number of variables which allows to draw conclusions in particular about specific moment theories like the regularized 13-moment equations.

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@Article{CiCP-18-529, author = {}, title = {Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {3}, pages = {529--557}, abstract = {

The accuracy of moment equations as approximations of kinetic gas theory is studied for four different boundary value problems. The kinetic setting is given by the BGK equation linearized around a globally constant Maxwellian using one space dimension and a three-dimensional velocity space. The boundary value problems include Couette and Poiseuille flow as well as heat conduction between walls and heat conduction based on a locally varying heating source. The polynomial expansion of the distribution function allows for different moment theories of which two popular families are investigated in detail. Furthermore, optimal approximations for a given number of variables are studied empirically. The paper focuses on approximations with relatively low number of variables which allows to draw conclusions in particular about specific moment theories like the regularized 13-moment equations.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.061013.160215a}, url = {http://global-sci.org/intro/article_detail/cicp/11039.html} }
TY - JOUR T1 - Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation JO - Communications in Computational Physics VL - 3 SP - 529 EP - 557 PY - 2018 DA - 2018/04 SN - 18 DO - http://doi.org/10.4208/cicp.061013.160215a UR - https://global-sci.org/intro/article_detail/cicp/11039.html KW - AB -

The accuracy of moment equations as approximations of kinetic gas theory is studied for four different boundary value problems. The kinetic setting is given by the BGK equation linearized around a globally constant Maxwellian using one space dimension and a three-dimensional velocity space. The boundary value problems include Couette and Poiseuille flow as well as heat conduction between walls and heat conduction based on a locally varying heating source. The polynomial expansion of the distribution function allows for different moment theories of which two popular families are investigated in detail. Furthermore, optimal approximations for a given number of variables are studied empirically. The paper focuses on approximations with relatively low number of variables which allows to draw conclusions in particular about specific moment theories like the regularized 13-moment equations.

Manuel Torrilhon. (2020). Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation. Communications in Computational Physics. 18 (3). 529-557. doi:10.4208/cicp.061013.160215a
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