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

Wei Su, Peng Wang, Yonghao Zhang

Research output: Contribution to journalArticlepeer-review


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
Article number335-342
JournalInternational journal of computational fluid dynamics
Issue number8
Publication statusPublished - 16 Sep 2019


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


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