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.
|Number of pages||12|
|Publication status||Published - 15 Jun 2018|
|Event||6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018 - Glasgow, United Kingdom|
Duration: 11 Jun 2018 → 15 Jun 2018
|Conference||6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018|
|Abbreviated title||ECCM - ECFD 2018|
|Period||11/06/18 → 15/06/18|
- hybridizable discontinuous galerkin
- Boltzmann equation
- kinetic model
- rarefied gas flow
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.