Two-Dimensional Simulation of Rarefied Gas Flows Using Quadrature-Based Moment Equations

2018 ◽  
Vol 16 (2) ◽  
pp. 1059-1084 ◽  
Author(s):  
Julian Koellermeier ◽  
Manuel Torrilhon
Keyword(s):  
Rarefied Gas ◽  
Gas Flows ◽  
Two Dimensional ◽  
Moment Equations ◽  
Rarefied Gas Flows ◽  
Dimensional Simulation

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 Entropic boundary conditions for 13 moment equations in rarefied gas flows

2019 ◽  
Vol 31 (2) ◽  
pp. 021215 ◽  
Author(s):  
Carl Philipp Zinner ◽  
Hans Christian Öttinger
Keyword(s):  
Boundary Conditions ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Moment Equations ◽  
Rarefied Gas Flows

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.

Shock polar investigation in supersonic rarefied gas flows over a circular cylinder

2021 ◽  
Vol 33 (5) ◽  
pp. 052006
Author(s):  
Hassan Akhlaghi ◽  
Ehsan Roohi ◽  
Abbas Daliri ◽  
Mohammad-Reza Soltani
Keyword(s):  
Circular Cylinder ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Rarefied Gas Flows
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