High-order hybridisable discontinuous Galerkin method for the gas kinetic equation

Wei Su, Peng Wang, Yonghao Zhang

Research output: Contribution to journalArticle

Abstract

The high-order hybridisable discontinuous Galerkin (HDG) method is used to find steady-state solution of gas kinetic equations on two-dimensional geometry. The velocity distribution function and its traces are approximated in piecewise polynomial space on triangular mesh and mesh skeleton, respectively. By employing a numerical flux derived from the upwind scheme and imposing its continuity on mesh skeleton, the global system for unknown traces is obtained with fewer coupled degrees of freedom, compared to the original DG method. The solutions of model equation for the Poiseuille flow through square channel show the higher order solver is faster than the lower order one. Moreover, the HDG scheme is more efficient than the original DG method when the degree of approximating polynomial is larger than 2. Finally, the developed scheme is extended to solve the Boltzmann equation with full collision operator, which can produce accurate results for shear-driven and thermally induced flows.
Original languageEnglish
Number of pages8
JournalInternational Journal of Computational Fluid Dynamics
Early online date16 Sep 2019
DOIs
Publication statusE-pub ahead of print - 16 Sep 2019

Fingerprint

Kinetic theory of gases
Galerkin method
Galerkin methods
kinetic equations
mesh
Polynomials
musculoskeletal system
Boltzmann equation
polynomials
Velocity distribution
gases
Distribution functions
Fluxes
laminar flow
continuity
Geometry
velocity distribution
degrees of freedom
distribution functions
shear

Keywords

  • hybridisable DG
  • Boltzmann equation
  • rarefied gas flow
  • upwind flux

Cite this

@article{639d34b5fa1443eaab4bc0a63dea2718,
title = "High-order hybridisable discontinuous Galerkin method for the gas kinetic equation",
abstract = "The high-order hybridisable discontinuous Galerkin (HDG) method is used to find steady-state solution of gas kinetic equations on two-dimensional geometry. The velocity distribution function and its traces are approximated in piecewise polynomial space on triangular mesh and mesh skeleton, respectively. By employing a numerical flux derived from the upwind scheme and imposing its continuity on mesh skeleton, the global system for unknown traces is obtained with fewer coupled degrees of freedom, compared to the original DG method. The solutions of model equation for the Poiseuille flow through square channel show the higher order solver is faster than the lower order one. Moreover, the HDG scheme is more efficient than the original DG method when the degree of approximating polynomial is larger than 2. Finally, the developed scheme is extended to solve the Boltzmann equation with full collision operator, which can produce accurate results for shear-driven and thermally induced flows.",
keywords = "hybridisable DG, Boltzmann equation, rarefied gas flow, upwind flux",
author = "Wei Su and Peng Wang and Yonghao Zhang",
year = "2019",
month = "9",
day = "16",
doi = "10.1080/10618562.2019.1666110",
language = "English",
journal = "International Journal of Computational Fluid Dynamics",
issn = "1061-8562",

}

TY - JOUR

T1 - High-order hybridisable discontinuous Galerkin method for the gas kinetic equation

AU - Su, Wei

AU - Wang, Peng

AU - Zhang, Yonghao

PY - 2019/9/16

Y1 - 2019/9/16

N2 - The high-order hybridisable discontinuous Galerkin (HDG) method is used to find steady-state solution of gas kinetic equations on two-dimensional geometry. The velocity distribution function and its traces are approximated in piecewise polynomial space on triangular mesh and mesh skeleton, respectively. By employing a numerical flux derived from the upwind scheme and imposing its continuity on mesh skeleton, the global system for unknown traces is obtained with fewer coupled degrees of freedom, compared to the original DG method. The solutions of model equation for the Poiseuille flow through square channel show the higher order solver is faster than the lower order one. Moreover, the HDG scheme is more efficient than the original DG method when the degree of approximating polynomial is larger than 2. Finally, the developed scheme is extended to solve the Boltzmann equation with full collision operator, which can produce accurate results for shear-driven and thermally induced flows.

AB - The high-order hybridisable discontinuous Galerkin (HDG) method is used to find steady-state solution of gas kinetic equations on two-dimensional geometry. The velocity distribution function and its traces are approximated in piecewise polynomial space on triangular mesh and mesh skeleton, respectively. By employing a numerical flux derived from the upwind scheme and imposing its continuity on mesh skeleton, the global system for unknown traces is obtained with fewer coupled degrees of freedom, compared to the original DG method. The solutions of model equation for the Poiseuille flow through square channel show the higher order solver is faster than the lower order one. Moreover, the HDG scheme is more efficient than the original DG method when the degree of approximating polynomial is larger than 2. Finally, the developed scheme is extended to solve the Boltzmann equation with full collision operator, which can produce accurate results for shear-driven and thermally induced flows.

KW - hybridisable DG

KW - Boltzmann equation

KW - rarefied gas flow

KW - upwind flux

U2 - 10.1080/10618562.2019.1666110

DO - 10.1080/10618562.2019.1666110

M3 - Article

JO - International Journal of Computational Fluid Dynamics

JF - International Journal of Computational Fluid Dynamics

SN - 1061-8562

ER -