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

2019 ◽  
Vol 9 (13) ◽  
pp. 2733
Author(s):  
Weiqi Yang ◽  
Shuo Tang ◽  
Hui Yang
Keyword(s):  
Moment Method ◽  
Rarefied Gas ◽  
Hermite Polynomials ◽  
Distribution Functions ◽  
Gas Flows ◽  
Thermally Induced ◽  
Rarefied Gas Flows ◽  
Discrete Velocity Method ◽  
The Moment ◽  
Non Equilibrium

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.

scholarly journals The Half-Range Moment Method in Harmonically Oscillating Rarefied Gas Flows

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 17
Author(s):  
Giorgos Tatsios ◽  
Alexandros Tsimpoukis ◽  
Dimitris Valougeorgis
Keyword(s):  
Boundary Conditions ◽  
Stokes Flow ◽  
Moment Method ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Moment Equations ◽  
Rarefied Gas Flows ◽  
Flow Parameters ◽  
Discrete Velocity Method ◽  
Wide Range

The formulation of the half-range moment method (HRMM), well defined in steady rarefied gas flows, is extended to linear oscillatory rarefied gas flows, driven by oscillating boundaries. The oscillatory Stokes (also known as Stokes second problem) and the oscillatory Couette flows, as representative ones for harmonically oscillating half-space and finite-medium flow setups respectively, are solved. The moment equations are derived from the linearized time-dependent BGK kinetic equation, operating accordingly over the positive and negative halves of the molecular velocity space. Moreover, the boundary conditions of the “positive” and “negative” moment equations are accordingly constructed from the half-range moments of the boundary conditions of the outgoing distribution function, assuming purely diffuse reflection. The oscillatory Stokes flow is characterized by the oscillation parameter, while the oscillatory Couette flow by the oscillation and rarefaction parameters. HRMM results for the amplitude and phase of the velocity and shear stress in a wide range of the flow parameters are presented and compared with corresponding results, obtained by the discrete velocity method (DVM). In the oscillatory Stokes flow the so-called penetration depth is also computed. When the oscillation frequency is lower than the collision frequency excellent agreement is observed, while when it is about the same or larger some differences are present. Overall, it is demonstrated that the HRMM can be applied to linear oscillatory rarefied gas flows, providing accurate results in a very wide range of the involved flow parameters. Since the computational effort is negligible, it is worthwhile to consider the efficient implementation of the HRMM to stationary and transient multidimensional rarefied gas flows.

scholarly journals Comparative study of the discrete velocity and the moment method for rarefied gas flows

2019 ◽  
Author(s):  
Weiqi Yang ◽  
Xiao-Jun Gu ◽  
David. Emerson ◽  
Yonghao Zhang ◽  
Shuo Tang
Keyword(s):  
Comparative Study ◽  
Moment Method ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Discrete Velocity ◽  
Rarefied Gas Flows ◽  
The Moment

A hybrid approach to couple the discrete velocity method and Method of Moments for rarefied gas flows

2020 ◽  
Vol 410 ◽  
pp. 109397 ◽  
Author(s):  
Weiqi Yang ◽  
Xiao-Jun Gu ◽  
Lei Wu ◽  
David R. Emerson ◽  
Yonghao Zhang ◽  
...  
Keyword(s):  
Method Of Moments ◽  
Rarefied Gas ◽  
Hybrid Approach ◽  
Gas Flows ◽  
Discrete Velocity ◽  
Rarefied Gas Flows ◽  
Discrete Velocity Method

Analysis of Rotational Non-equilibrium in Rarefied Gas Flows by REMPI

2004 ◽  
Vol 2004.7 (0) ◽  
pp. 35-36
Author(s):  
Hideo MORI ◽  
Tomohide NIIMI ◽  
Isao AKIYAMA ◽  
Takumi TSUZUKI
Keyword(s):  
Rarefied Gas ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Non Equilibrium

scholarly journals Modelling Thermally Induced Non-Equilibrium Gas Flows by Coupling Kinetic and Extended Thermodynamic Methods

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 816 ◽  
Author(s):  
Weiqi Yang ◽  
Xiao-Jun Gu ◽  
David R. Emerson ◽  
Yonghao Zhang ◽  
Shuo Tang
Keyword(s):  
Flow Region ◽  
Equation System ◽  
Moment Equation ◽  
Gas Flows ◽  
Thermally Induced ◽  
Temperature Discontinuity ◽  
Discrete Velocity Method ◽  
Extended Thermodynamic ◽  
Induced Flow ◽  
Non Equilibrium

Thermally induced non-equilibrium gas flows have been simulated in the present study by coupling kinetic and extended thermodynamic methods. Three different types of thermally induced gas flows, including temperature-discontinuity- and temperature-gradient-induced flows and radiometric flow, have been explored in the transition regime. The temperature-discontinuity-induced flow case has shown that as the Knudsen number increases, the regularised 26 (R26) moment equation system will gradually loss its accuracy and validation. A coupling macro- and microscopic approach is employed to overcome these problems. The R26 moment equations are used at the macroscopic level for the bulk flow region, while the kinetic equation associated with the discrete velocity method (DVM) is applied to describe the gas close to the wall at the microscopic level, which yields a hybrid DVM/R26 approach. The numerical results have shown that the hybrid DVM/R26 method can be faithfully used for the thermally induced non-equilibrium flows. The proposed scheme not only improves the accuracy of the results in comparison with the R26 equations, but also extends their capability with a wider range of Knudsen numbers. In addition, the hybrid scheme is able to reduce the computational memory and time cost compared to the DVM.

Analysis of non-equilibrium rarefied gas flows induced by evaporation from nanoporous membranes

2021 ◽  
Vol 2021.27 (0) ◽  
pp. 10C03
Author(s):  
Hiroki IMAI ◽  
Yuta SASAKI ◽  
Hiroshi MATSUMOTO ◽  
Yuta YOSHIMOTO ◽  
Shu TAKAGI ◽  
...  
Keyword(s):  
Rarefied Gas ◽  
Gas Flows ◽  
Nanoporous Membranes ◽  
Rarefied Gas Flows ◽  
Non Equilibrium

scholarly journals On the accuracy of macroscopic equations for linearized rarefied gas flows

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Lei Wu ◽  
Xiao-Jun Gu
Keyword(s):  
Boltzmann Equation ◽  
Volume Diffusion ◽  
Rarefied Gas ◽  
Hermite Polynomials ◽  
Velocity Distribution Function ◽  
Gas Flows ◽  
Burnett Equations ◽  
Moment Equations ◽  
Rarefied Gas Flows ◽  
Macroscopic Equations

AbstractMany macroscopic equations are proposed to describe the rarefied gas dynamics beyond the Navier-Stokes level, either from the mesoscopic Boltzmann equation or some physical arguments, including (i) Burnett, Woods, super-Burnett, augmented Burnett equations derived from the Chapman-Enskog expansion of the Boltzmann equation, (ii) Grad 13, regularized 13/26 moment equations, rational extended thermodynamics equations, and generalized hydrodynamic equations, where the velocity distribution function is expressed in terms of low-order moments and Hermite polynomials, and (iii) bi-velocity equations and “thermo-mechanically consistent" Burnett equations based on the argument of “volume diffusion”. This paper is dedicated to assess the accuracy of these macroscopic equations. We first consider the Rayleigh-Brillouin scattering, where light is scattered by the density fluctuation in gas. In this specific problem macroscopic equations can be linearized and solutions can always be obtained, no matter whether they are stable or not. Moreover, the accuracy assessment is not contaminated by the gas-wall boundary condition in this periodic problem. Rayleigh-Brillouin spectra of the scattered light are calculated by solving the linearized macroscopic equations and compared to those from the linearized Boltzmann equation. We find that (i) the accuracy of Chapman-Enskog expansion does not always increase with the order of expansion, (ii) for the moment method, the more moments are included, the more accurate the results are, and (iii) macroscopic equations based on “volume diffusion" do not work well even when the Knudsen number is very small. Therefore, among about a dozen tested equations, the regularized 26 moment equations are the most accurate. However, for moderate and highly rarefied gas flows, huge number of moments should be included, as the convergence to true solutions is rather slow. The same conclusion is drawn from the problem of sound propagation between the transducer and receiver. This slow convergence of moment equations is due to the incapability of Hermite polynomials in the capturing of large discontinuities and rapid variations of the velocity distribution function. This study sheds some light on how to choose/develop macroscopic equations for rarefied gas dynamics.

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