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Abstract
The mass flow rate of Poiseuille flow of rarefied gas through long ducts of twodimensional crosssections with arbitrary shape is critical in the porenetwork modeling of gas transport in porous media. Here, for the first time, the highorder hybridizable discontinuous Galerkin (HDG) method is used to find the steadystate solution of the linearized Bhatnagar–Gross–Krook equation on twodimensional triangular meshes. The velocity distribution function and its traces are approximated in piecewise polynomial spaces (of degree up to 4) on the triangular meshes and mesh skeletons, respectively. By employing a numerical flux that is derived from the firstorder upwind scheme and imposing its continuity weakly on the mesh skeletons, global systems for unknown traces are obtained with fewer coupled degrees of freedom when compared to the original discontinuous Galerkin formulation. To achieve fast convergence to the steadystate solution, a diffusionlike equation for flow velocity, which is asymptoticpreserving into the fluid dynamic limit, is solved by the HDG simultaneously on the same meshes. The proposed HDGsynthetic iterative scheme is proved to be accurate and efficient. Specifically, for flows in the nearcontinuum regime, numerical simulations have shown that, to achieve the same level of accuracy, our scheme could be faster than the conventional iterative scheme by two orders of magnitude, also it is faster than the synthetic iterative scheme based on the finite difference discretization in the spatial space by one order of magnitude. In addition, the implicit HDG method is more efficient than an explicit discontinuous Galerkin gas kinetic solver, as well as the implicit discontinuous Galerkin scheme when the degree of approximating polynomial is larger than 2. The HDGsynthetic iterative scheme is ready to be extended to simulate rarefied gas mixtures and the Boltzmann collision operator.
Original language  English 

Pages (fromto)  973991 
Number of pages  19 
Journal  Journal of Computational Physics 
Volume  376 
Early online date  1 Sep 2018 
DOIs  
Publication status  Published  1 Jan 2019 
Keywords
 hybridizable discontinuous Galerkin
 gas kinetic equation
 synthetic iterative scheme
 fast convergence
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Projects
 1 Finished

PoreScale Study of Gas Flows in Ultratight Porous Media
Zhang, Y. & Scanlon, T.
EPSRC (Engineering and Physical Sciences Research Council)
1/09/15 → 30/09/19
Project: Research