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

Su, Wei and Wang, Peng and Zhang, Yonghao and Wu, Lei (2018) A high-order hybridizable discontinuous galerkin method for gas kinetic equation. In: 6th European Conference on Computational Mechanics and 7th European Conference on Computational Fluid Dynamics 2018, 2018-06-11 - 2018-06-15.

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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.