A Direct Solver for Initial Value Problems of Rarefied Gas Flows of Arbitrary Statistics

2013 ◽  
Vol 14 (1) ◽  
pp. 242-264 ◽  
Author(s):  
Jaw-Yen Yang ◽  
Bagus Putra Muljadi ◽  
Zhi-Hui Li ◽  
Han-Xin Zhang
Keyword(s):  
Distribution Function ◽  
Initial Value Problems ◽  
Rarefied Gas ◽  
Relaxation Times ◽  
Velocity Distribution Function ◽  
Gas Flows ◽  
Good Resolution ◽  
Initial Value ◽  
Rarefied Gas Flows ◽  
Wide Range

AbstractAn accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three statistics. The discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term. The high order weighted essentially non-oscillatory scheme is then implemented to capture the time evolution of the discretized velocity distribution function in physical space and time. The method is developed for two space dimensions and implemented on gas particles that obey the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. Computational examples in one- and two-dimensional initial value problems of rarefied gas flows are presented and the results indicating good resolution of the main flow features can be achieved. Flows of wide range of relaxation times and Knudsen numbers covering different flow regimes are computed to validate the robustness of the method. The recovery of quantum statistics to the classical limit is also tested for small fugacity values.

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.

Thermal Lattice Boltzmann Simulation of Rarefied Gas Flows in Nanochannels for Wide Range of Knudsen Number

2011 ◽  
Vol 403-408 ◽  
pp. 5313-5317
Author(s):  
A.H. Meghdadi Isfahani ◽  
A. Soleimani
Keyword(s):  
Lattice Boltzmann ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Knudsen Numbers ◽  
Lattice Boltzmann Simulation ◽  
Wide Range ◽  
Flow Through ◽  
Boltzmann Method ◽  
Thermal Lattice Boltzmann

Using a modified Lattice Boltzmann Method (LBM), developing thermal flow through micro and nano channels has been modeled. Based on the improving of the dynamic viscosity and thermal conductivity, an effective relaxation time formulation is proposed which is able to simulate wide range of Knudsen numbers, Kn,. The results show that in spite of the standard LBM, the temperature distributions and the local Nusselt number obtained from this modified thermal LBM, agree well with the other numerical and empirical results in a wide range of Knudsen numbers.

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

scholarly journals Rarefied gas flows through meshes and implications for atmospheric measurements

2001 ◽  
Vol 19 (5) ◽  
pp. 563-569 ◽  
Author(s):  
J. Gumbel
Keyword(s):  
Middle Atmosphere ◽  
Rarefied Gas ◽  
Direct Simulation Monte Carlo ◽  
Atmospheric Composition ◽  
Gas Flows ◽  
Atmospheric Measurements ◽  
Rarefied Gas Flows ◽  
Flow Disturbances ◽  
Composition And Structure ◽  
Compression Effects

Abstract. Meshes are commonly used as part of instruments for in situ atmospheric measurements. This study analyses the aerodynamic effect of meshes by means of wind tunnel experiments and numerical simulations. Based on the Direct Simulation Monte Carlo method, a simple mesh parameterisation is described and applied to a number of representative flow conditions. For open meshes freely exposed to the flow, substantial compression effects are found both upstream and downstream of the mesh. Meshes attached to close instrument structures, on the other hand, cause only minor flow disturbances. In an accompanying paper, the approach developed here is applied to the quantitative analysis of rocket-borne density measurements in the middle atmosphere.Key words. Atmospheric composition and structure (instruments and techniques; middle atmosphere – composition and chemistry)

scholarly journals An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries

2010 ◽  
Vol 39 (10) ◽  
pp. 2078-2089 ◽  
Author(s):  
T.J. Scanlon ◽  
E. Roohi ◽  
C. White ◽  
M. Darbandi ◽  
J.M. Reese
Keyword(s):  
Open Source ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Arbitrary Geometries
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