Abstract
In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely employed to solve the gas kinetic equations. However, it is usually computationally expensive in dealing with complex geometry and high Mach number flows. In the present work, both classical third-order time implicit DVM and the moment method are employed in finding steady-state solutions of the force-driven Poiseuille flow and flow past a circle cylinder. Their performance, in terms of accuracy, has been compared and analyzed. Choosing the velocity distribution functions (VDFs) obtained from DVM solutions as the benchmark, we reconstruct the expanded VDFs using regularized 13 moment equations (R13) and regularized 26 moment equations (R26) and then compare the accuracy of the expanded VDFs with different order of Hermite polynomial expansions. From the computed velocity profiles and reconstructed VDFs, we have found that the moment method can extend the macroscopic equations into the early transition regime, and the R26 can relatively accurately represent the characteristics of the VDFs in comparison with the gas kinetic model. Conversely, the Navier-Stokes-Fourier (NSF) equations are not able to produce an accurate description of the expanded distribution functions.
| Language | English |
|---|---|
| Article number | 120006 |
| Number of pages | 9 |
| Journal | AIP Conference Proceedings |
| Volume | 2132 |
| DOIs | |
| Publication status | Published - 5 Aug 2019 |
| Event | 31st International Symposium on Rarefied Gas Dynamics, RGD 2018 - Glasgow, United Kingdom Duration: 23 Jul 2018 → 27 Jul 2018 |
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Keywords
- rarefied gas dynamics
- discrete velocity method
- DVM
- velocity distribution functions
- VDF
- gas kinetic model
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Comparative study of the discrete velocity and the moment method for rarefied gas flows. / Yang, Weiqi; Gu, Xiao Jun; Emerson, David; Zhang, Yonghao; Tang, Shuo.
In: AIP Conference Proceedings, Vol. 2132, 120006, 05.08.2019.Research output: Contribution to journal › Conference Contribution
TY - JOUR
T1 - Comparative study of the discrete velocity and the moment method for rarefied gas flows
AU - Yang, Weiqi
AU - Gu, Xiao Jun
AU - Emerson, David
AU - Zhang, Yonghao
AU - Tang, Shuo
PY - 2019/8/5
Y1 - 2019/8/5
N2 - In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely employed to solve the gas kinetic equations. However, it is usually computationally expensive in dealing with complex geometry and high Mach number flows. In the present work, both classical third-order time implicit DVM and the moment method are employed in finding steady-state solutions of the force-driven Poiseuille flow and flow past a circle cylinder. Their performance, in terms of accuracy, has been compared and analyzed. Choosing the velocity distribution functions (VDFs) obtained from DVM solutions as the benchmark, we reconstruct the expanded VDFs using regularized 13 moment equations (R13) and regularized 26 moment equations (R26) and then compare the accuracy of the expanded VDFs with different order of Hermite polynomial expansions. From the computed velocity profiles and reconstructed VDFs, we have found that the moment method can extend the macroscopic equations into the early transition regime, and the R26 can relatively accurately represent the characteristics of the VDFs in comparison with the gas kinetic model. Conversely, the Navier-Stokes-Fourier (NSF) equations are not able to produce an accurate description of the expanded distribution functions.
AB - In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely employed to solve the gas kinetic equations. However, it is usually computationally expensive in dealing with complex geometry and high Mach number flows. In the present work, both classical third-order time implicit DVM and the moment method are employed in finding steady-state solutions of the force-driven Poiseuille flow and flow past a circle cylinder. Their performance, in terms of accuracy, has been compared and analyzed. Choosing the velocity distribution functions (VDFs) obtained from DVM solutions as the benchmark, we reconstruct the expanded VDFs using regularized 13 moment equations (R13) and regularized 26 moment equations (R26) and then compare the accuracy of the expanded VDFs with different order of Hermite polynomial expansions. From the computed velocity profiles and reconstructed VDFs, we have found that the moment method can extend the macroscopic equations into the early transition regime, and the R26 can relatively accurately represent the characteristics of the VDFs in comparison with the gas kinetic model. Conversely, the Navier-Stokes-Fourier (NSF) equations are not able to produce an accurate description of the expanded distribution functions.
KW - rarefied gas dynamics
KW - discrete velocity method
KW - DVM
KW - velocity distribution functions
KW - VDF
KW - gas kinetic model
U2 - 10.1063/1.5119619
DO - 10.1063/1.5119619
M3 - Conference Contribution
VL - 2132
JO - AIP Conference Proceedings
T2 - AIP Conference Proceedings
JF - AIP Conference Proceedings
SN - 0094-243X
M1 - 120006
ER -