Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation. (14th September 2015)

• Record Type: Journal Article
• Authors: Torrilhon, Manuel
• Is Part Of: Communications in computational physics. Volume 18:Number 3(2015:Sep.)
• Page Start: 529
• Page End: 557
• Publication Date: 2015-09-14
• Subjects: 82B40, -- 76P05, -- 35L65; Kinetic gas theory, -- Hermite expansion, -- channel flow; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.061013.160215a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.