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Open AccessArticle

Analysis of the Moment Method and the Discrete Velocity Method in Modeling Non-Equilibrium Rarefied Gas Flows: A Comparative Study

by Weiqi Yang 1, Shuo Tang 1 and Hui Yang 2,*
1
School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China
2
School of Computer, National University of Defense Technology, Changsha 410073, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(13), 2733; https://doi.org/10.3390/app9132733
Received: 23 May 2019 / Revised: 29 June 2019 / Accepted: 3 July 2019 / Published: 5 July 2019
In the present study, the performance of the moment method, in terms of accuracy and computational efficiency, was evaluated at both the macro- and microscopic levels. Three different types of non-equilibrium gas flows, including the force-driven Poiseuille flow, lid-driven and thermally induced cavity flows, were simulated in the slip and transition regimes. Choosing the flow fields obtained from the Boltzmann model equation as the benchmark, the accuracy and validation of Navier–Stokes–Fourier (NSF), regularized 13 (R13) and regularized 26 (R26) equations were explored at the macroscopic level. Meanwhile, we reconstructed the velocity distribution functions (VDFs) using the Hermite polynomials with different-order of molecular velocity moments, and compared them with the Boltzmann solutions at the microscopic level. Moreover, we developed a kinetic criterion to indirectly assess the errors of the reconstructed VDFs. The results have shown that the R13 and R26 moment methods can be faithfully used for non-equilibrium rarefied gas flows in the slip and transition regimes. However, as indicated from the thermally induced case, all of the reconstructed VDFs are still very close to the equilibrium state, and none of them can reproduce the accurate VDF profile when the Knudsen number is above 0.5. View Full-Text
Keywords: R13 moment method; R26 moment method; slip regime; transition regime; discrete velocity method R13 moment method; R26 moment method; slip regime; transition regime; discrete velocity method
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Yang, W.; Tang, S.; Yang, H. Analysis of the Moment Method and the Discrete Velocity Method in Modeling Non-Equilibrium Rarefied Gas Flows: A Comparative Study. Appl. Sci. 2019, 9, 2733.

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