A high-order hybridizable discontinuous galerkin method for gas kinetic equation

Wei Su, Peng Wang, Yonghao Zhang, Lei Wu

Research output: Contribution to conferencePaper

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Abstract

The high-order hybridizable discontinuous Galerkin method is used to find the steady-state solution of the linearized Shakhov kinetic model equations on two-dimensional triangular meshes. The perturbed velocity distribution function and its traces are approximated in the piece- wise polynomial space on the triangular meshes and the mesh skeletons, respectively. By employing a numerical flux that is derived from the first- order upwind scheme and imposing its continuity on the mesh skeletons, global systems for unknown traces are obtained with a few coupled degrees of freedom. The steady-state solution is reached through an implicit iterative scheme. Verification is carried out for a two-dimensional thermal conduction problem. Results show that the higher-order solver is more efficient than the lower-order one. The proposed scheme is ready to extended to simulate the full Boltzmann collision operator.
Original languageEnglish
Number of pages12
Publication statusPublished - 15 Jun 2018
Event6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018 - Glasgow, United Kingdom
Duration: 11 Jun 201815 Jun 2018

Conference

Conference6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018
Abbreviated titleECCM - ECFD 2018
CountryUnited Kingdom
CityGlasgow
Period11/06/1815/06/18

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Kinetic theory of gases
Galerkin methods
Velocity distribution
Distribution functions
Polynomials
Fluxes
Kinetics
Hot Temperature

Keywords

  • hybridizable discontinuous galerkin
  • Boltzmann equation
  • kinetic model
  • rarefied gas flow

Cite this

Su, W., Wang, P., Zhang, Y., & Wu, L. (2018). A high-order hybridizable discontinuous galerkin method for gas kinetic equation. Paper presented at 6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018, Glasgow, United Kingdom.
Su, Wei ; Wang, Peng ; Zhang, Yonghao ; Wu, Lei. / A high-order hybridizable discontinuous galerkin method for gas kinetic equation. Paper presented at 6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018, Glasgow, United Kingdom.12 p.
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Su, W, Wang, P, Zhang, Y & Wu, L 2018, 'A high-order hybridizable discontinuous galerkin method for gas kinetic equation' Paper presented at 6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018, Glasgow, United Kingdom, 11/06/18 - 15/06/18, .

A high-order hybridizable discontinuous galerkin method for gas kinetic equation. / Su, Wei; Wang, Peng; Zhang, Yonghao; Wu, Lei.

2018. Paper presented at 6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018, Glasgow, United Kingdom.

Research output: Contribution to conferencePaper

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N2 - The high-order hybridizable discontinuous Galerkin method is used to find the steady-state solution of the linearized Shakhov kinetic model equations on two-dimensional triangular meshes. The perturbed velocity distribution function and its traces are approximated in the piece- wise polynomial space on the triangular meshes and the mesh skeletons, respectively. By employing a numerical flux that is derived from the first- order upwind scheme and imposing its continuity on the mesh skeletons, global systems for unknown traces are obtained with a few coupled degrees of freedom. The steady-state solution is reached through an implicit iterative scheme. Verification is carried out for a two-dimensional thermal conduction problem. Results show that the higher-order solver is more efficient than the lower-order one. The proposed scheme is ready to extended to simulate the full Boltzmann collision operator.

AB - The high-order hybridizable discontinuous Galerkin method is used to find the steady-state solution of the linearized Shakhov kinetic model equations on two-dimensional triangular meshes. The perturbed velocity distribution function and its traces are approximated in the piece- wise polynomial space on the triangular meshes and the mesh skeletons, respectively. By employing a numerical flux that is derived from the first- order upwind scheme and imposing its continuity on the mesh skeletons, global systems for unknown traces are obtained with a few coupled degrees of freedom. The steady-state solution is reached through an implicit iterative scheme. Verification is carried out for a two-dimensional thermal conduction problem. Results show that the higher-order solver is more efficient than the lower-order one. The proposed scheme is ready to extended to simulate the full Boltzmann collision operator.

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KW - rarefied gas flow

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Su W, Wang P, Zhang Y, Wu L. A high-order hybridizable discontinuous galerkin method for gas kinetic equation. 2018. Paper presented at 6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018, Glasgow, United Kingdom.