Convergence Study of Moment Approximations for Boundary Value Problems of the Boltzmann-BGK Equation
Year: 2015
Communications in Computational Physics, Vol. 18 (2015), Iss. 3 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.061013.160215a
Communications in Computational Physics, Vol. 18 (2015), Iss. 3 : pp. 529–557
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
-
Moment method for the Boltzmann equation of reactive quaternary gaseous mixture
Sarna, Neeraj | Oblapenko, Georgii | Torrilhon, ManuelPhysica A: Statistical Mechanics and its Applications, Vol. 574 (2021), Iss. P.125874
https://doi.org/10.1016/j.physa.2021.125874 [Citations: 2] -
On the Holway-Weiss debate: Convergence of the Grad-moment-expansion in kinetic gas theory
Cai, Zhenning | Torrilhon, ManuelPhysics of Fluids, Vol. 31 (2019), Iss. 12
https://doi.org/10.1063/1.5127114 [Citations: 17] -
A positive and stable L2-minimization based moment method for the Boltzmann equation of gas dynamics
Sarna, Neeraj
Journal of Computational Physics, Vol. 440 (2021), Iss. P.110428
https://doi.org/10.1016/j.jcp.2021.110428 [Citations: 1] -
Moment models for neutral particles in high-collisional regimes for plasma edge simulations
Lopez, Luis Fernando Cusicanqui | Koellermeier, Julian | Maes, Vince | Samaey, Giovanni2ND INTERNATIONAL CONFERENCE ON ADVANCED EARTH SCIENCE AND FOUNDATION ENGINEERING (ICASF 2023): Advanced Earth Science and Foundation Engineering, (2024), P.190002
https://doi.org/10.1063/5.0187540 [Citations: 0] -
Projective integration schemes for hyperbolic moment equations
Koellermeier, Julian | Samaey, GiovanniKinetic & Related Models, Vol. 14 (2021), Iss. 2 P.353
https://doi.org/10.3934/krm.2021008 [Citations: 7] -
14-moment maximum-entropy modeling of collisionless ions for Hall thruster discharges
Boccelli, S. | McDonald, J. G. | Magin, T. E.Physics of Plasmas, Vol. 29 (2022), Iss. 8
https://doi.org/10.1063/5.0100092 [Citations: 6] -
A 14-moment maximum-entropy description of electrons in crossed electric and magnetic fields
Boccelli, S. | Giroux, F. | Magin, T. E. | Groth, C. P. T. | McDonald, J. G.Physics of Plasmas, Vol. 27 (2020), Iss. 12
https://doi.org/10.1063/5.0025651 [Citations: 17] -
Two-Dimensional Simulation of Rarefied Gas Flows Using Quadrature-Based Moment Equations
Koellermeier, Julian | Torrilhon, ManuelMultiscale Modeling & Simulation, Vol. 16 (2018), Iss. 2 P.1059
https://doi.org/10.1137/17M1147548 [Citations: 11] -
Higher-order moment theories for dilute granular gases of smooth hard spheres
Gupta, Vinay Kumar | Shukla, Priyanka | Torrilhon, ManuelJournal of Fluid Mechanics, Vol. 836 (2018), Iss. P.451
https://doi.org/10.1017/jfm.2017.806 [Citations: 15] -
Moment method as a numerical solver: Challenge from shock structure problems
Cai, Zhenning
Journal of Computational Physics, Vol. 444 (2021), Iss. P.110593
https://doi.org/10.1016/j.jcp.2021.110593 [Citations: 4] -
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
Rana, Anirudh Singh | Struchtrup, HenningPhysics of Fluids, Vol. 28 (2016), Iss. 2
https://doi.org/10.1063/1.4941293 [Citations: 40] -
Hierarchical Boltzmann simulations and model error estimation
Torrilhon, Manuel | Sarna, NeerajJournal of Computational Physics, Vol. 342 (2017), Iss. P.66
https://doi.org/10.1016/j.jcp.2017.04.041 [Citations: 21] -
Simultaneous-approximation-term based boundary discretization for moment equations of rarefied gas dynamics
Sarna, Neeraj | Kapadia, Harshit | Torrilhon, ManuelJournal of Computational Physics, Vol. 407 (2020), Iss. P.109243
https://doi.org/10.1016/j.jcp.2020.109243 [Citations: 4] -
An ultra-sparse approximation of kinetic solutions to spatially homogeneous flows of non-continuum gas
Alekseenko, Alexander | Grandilli, Amy | Wood, AihuaResults in Applied Mathematics, Vol. 5 (2020), Iss. P.100085
https://doi.org/10.1016/j.rinam.2019.100085 [Citations: 2] -
Evaporation boundary conditions for the R13 equations of rarefied gas dynamics
Struchtrup, Henning | Beckmann, Alexander | Rana, Anirudh Singh | Frezzotti, AldoPhysics of Fluids, Vol. 29 (2017), Iss. 9
https://doi.org/10.1063/1.4989570 [Citations: 27] -
Burnett Spectral Method for High-Speed Rarefied Gas Flows
Hu, Zhicheng | Cai, ZhenningSIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 5 P.B1193
https://doi.org/10.1137/19M1294010 [Citations: 10] -
Accelerating the Convergence of the Moment Method for the Boltzmann Equation Using Filters
Fan, Yuwei | Koellermeier, JulianJournal of Scientific Computing, Vol. 84 (2020), Iss. 1
https://doi.org/10.1007/s10915-020-01251-8 [Citations: 16] -
On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation
Sarna, Neeraj | Torrilhon, ManuelJournal of Statistical Physics, Vol. 170 (2018), Iss. 1 P.101
https://doi.org/10.1007/s10955-017-1910-z [Citations: 20] -
Structured derivation of moment equations and stable boundary conditions with an introduction to symmetric, trace-free tensors
Bünger, Jonas | Christhuraj, Edilbert | Hanke, Andrea | Torrilhon, ManuelKinetic and Related Models, Vol. 16 (2023), Iss. 3 P.458
https://doi.org/10.3934/krm.2022035 [Citations: 6] -
Entropy stable Hermite approximation of the linearised Boltzmann equation for inflow and outflow boundaries
Sarna, Neeraj | Torrilhon, ManuelJournal of Computational Physics, Vol. 369 (2018), Iss. P.16
https://doi.org/10.1016/j.jcp.2018.04.050 [Citations: 8] -
Convergence Analysis of Grad's Hermite Expansion for Linear Kinetic Equations
Sarna, Neeraj | Giesselmann, Jan | Torrilhon, ManuelSIAM Journal on Numerical Analysis, Vol. 58 (2020), Iss. 2 P.1164
https://doi.org/10.1137/19M1270884 [Citations: 9] -
Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory
Beckmann, Alexander Felix | Rana, Anirudh Singh | Torrilhon, Manuel | Struchtrup, HenningEntropy, Vol. 20 (2018), Iss. 9 P.680
https://doi.org/10.3390/e20090680 [Citations: 12] -
Linear Stability of Hyperbolic Moment Models for Boltzmann Equation
Di, Yana | Fan, Yuwei | Li, Ruo | Zheng, LingchaoNumerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 2 P.255
https://doi.org/10.4208/nmtma.2017.s04 [Citations: 14] -
Spline moment models for the one-dimensional Boltzmann–Bhatnagar–Gross–Krook equation
Koellermeier, Julian | Scholz, UllikaPhysics of Fluids, Vol. 32 (2020), Iss. 10
https://doi.org/10.1063/5.0020998 [Citations: 4] -
Moment theories for a -dimensional dilute granular gas of Maxwell molecules
Gupta, Vinay Kumar
Journal of Fluid Mechanics, Vol. 888 (2020), Iss.
https://doi.org/10.1017/jfm.2020.20 [Citations: 5] -
Model order reduction for the 1D Boltzmann-BGK equation: identifying intrinsic variables using neural networks
Koellermeier, Julian | Krah, Philipp | Reiss, Julius | Schellin, ZacharyMicrofluidics and Nanofluidics, Vol. 28 (2024), Iss. 3
https://doi.org/10.1007/s10404-024-02711-5 [Citations: 0] -
Linear Regularized 13-Moment Equations with Onsager Boundary Conditions for General Gas Molecules
Cai, Zhenning | Torrilhon, Manuel | Yang, SiyaoSIAM Journal on Applied Mathematics, Vol. 84 (2024), Iss. 1 P.215
https://doi.org/10.1137/23M1556472 [Citations: 0] -
Numerical Simulation of Microflows Using Moment Methods with Linearized Collision Operator
Cai, Zhenning | Torrilhon, ManuelJournal of Scientific Computing, Vol. 74 (2018), Iss. 1 P.336
https://doi.org/10.1007/s10915-017-0442-7 [Citations: 22]