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

Wei Su, Peng Wang, Yonghao Zhang, Lei Wu

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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

Keywords

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

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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.