Year: 2017
Communications in Computational Physics, Vol. 21 (2017), Iss. 4 : pp. 981–1011
Abstract
Moment models are often used for the solution of kinetic equations such
as the Boltzmann equation. Unfortunately, standard models like Grad's equations are
not hyperbolic and can lead to nonphysical solutions. Newly derived moment models
like the Hyperbolic Moment Equations and the Quadrature-Based Moment Equations
yield globally hyperbolic equations but are given in partially conservative form that
cannot be written as a conservative system.
In this paper we investigate the applicability of different dedicated numerical
schemes to solve the partially conservative model equations. Caused by the non-conservative
type of equation we obtain differences in the numerical solutions, but
due to the structure of the moment systems we show that these effects are very small
for standard simulation cases. After successful identification of useful numerical settings
we show a convergence study for a shock tube problem and compare the results
to a discrete velocity solution. The results are in good agreement with the reference
solution and we see convergence considering an increasing number of moments.
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.OA-2016-0053
Communications in Computational Physics, Vol. 21 (2017), Iss. 4 : pp. 981–1011
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
-
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] -
Efficient moment method for modeling nanoporous evaporation
De Fraja, Thomas C. | Rana, Anirudh S. | Enright, Ryan | Cooper, Laura J. | Lockerby, Duncan A. | Sprittles, James E.Physical Review Fluids, Vol. 7 (2022), Iss. 2
https://doi.org/10.1103/PhysRevFluids.7.024201 [Citations: 7] -
On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems
Pimentel-García, Ernesto | Parés, Carlos | Castro, Manuel J. | Koellermeier, JulianApplied Mathematics and Computation, Vol. 388 (2021), Iss. P.125544
https://doi.org/10.1016/j.amc.2020.125544 [Citations: 0] -
Computational Science – ICCS 2020
Projective Integration for Moment Models of the BGK Equation
Koellermeier, Julian | Samaey, Giovanni2020
https://doi.org/10.1007/978-3-030-50433-5_25 [Citations: 1] -
Error estimators for adaptive simulation of rarefied gases using hyperbolic moment models
Koellermeier, Julian
31ST INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS: RGD31, (2019), P.120004
https://doi.org/10.1063/1.5119617 [Citations: 1] -
Machine learning moment closure models for the radiative transfer equation I: Directly learning a gradient based closure
Huang, Juntao | Cheng, Yingda | Christlieb, Andrew J. | Roberts, Luke F.Journal of Computational Physics, Vol. 453 (2022), Iss. P.110941
https://doi.org/10.1016/j.jcp.2022.110941 [Citations: 14] -
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] -
Hermite spectral method for multi-species Boltzmann equation
Li, Ruo | Lu, Yixiao | Wang, Yanli | Xu, HaoxuanJournal of Computational Physics, Vol. 471 (2022), Iss. P.111650
https://doi.org/10.1016/j.jcp.2022.111650 [Citations: 3] -
Aggregation and disaggregation of active particles on the unit sphere with time-dependent frequencies
Kim, Dohyun | Kim, JeonghoDiscrete & Continuous Dynamical Systems - B, Vol. 27 (2022), Iss. 4 P.2247
https://doi.org/10.3934/dcdsb.2021131 [Citations: 0] -
Hyperbolic Problems: Theory, Numerics, Applications. Volume II
Numerical Approximation of a Simplified Kinetic Model for a Sedimenting Suspension of Rod-Like Particles Using Hyperbolic Systems of Moment Equations
Dahm, Sina | Helzel, Christiane2024
https://doi.org/10.1007/978-3-031-55264-9_29 [Citations: 0] -
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] -
Spatially Adaptive Projective Integration Schemes For Stiff Hyperbolic Balance Laws With Spectral Gaps
Koellermeier, Julian | Samaey, GiovanniThe SMAI Journal of computational mathematics, Vol. 8 (2022), Iss. P.295
https://doi.org/10.5802/smai-jcm.88 [Citations: 1] -
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] -
Entropy bounds for the space–time discontinuous Galerkin finite element moment method applied to the BGK–Boltzmann equation
Abdelmalik, M.R.A. | van der Woude, D.A.M. | van Brummelen, E.H.Computer Methods in Applied Mechanics and Engineering, Vol. 398 (2022), Iss. P.115162
https://doi.org/10.1016/j.cma.2022.115162 [Citations: 1] -
Hierarchical micro-macro acceleration for moment models of kinetic equations
Koellermeier, Julian | Vandecasteele, HannesJournal of Computational Physics, Vol. 488 (2023), Iss. P.112194
https://doi.org/10.1016/j.jcp.2023.112194 [Citations: 1] -
An Approximation for the Twenty-One-Moment Maximum-Entropy Model of Rarefied Gas Dynamics
Giroux, Fabien | McDonald, James G.International Journal of Computational Fluid Dynamics, Vol. 35 (2021), Iss. 8 P.632
https://doi.org/10.1080/10618562.2022.2047666 [Citations: 6] -
Theory, Numerics and Applications of Hyperbolic Problems II
Simplified Hyperbolic Moment Equations
Koellermeier, Julian | Torrilhon, Manuel2018
https://doi.org/10.1007/978-3-319-91548-7_17 [Citations: 0] -
Hermite Spectral Method for Multi-Species Boltzmann Equation
Li, Ruo | Lu, Yixiao | Wang, Yanli | Xu, HaoxuanSSRN Electronic Journal , Vol. (2022), Iss.
https://doi.org/10.2139/ssrn.4062737 [Citations: 1] -
fenicsR13
Theisen, Lambert | Torrilhon, ManuelACM Transactions on Mathematical Software, Vol. 47 (2021), Iss. 2 P.1
https://doi.org/10.1145/3442378 [Citations: 4] -
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] -
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] -
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] -
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]