scholarly journals A Fokker–Planck Model of the Boltzmann Equation with Correct Prandtl Number for Polyatomic Gases

2017 ◽  
Vol 168 (5) ◽  
pp. 1031-1055 ◽  
Author(s):  
J. Mathiaud ◽  
L. Mieussens
Keyword(s):  
Boltzmann Equation ◽  
Prandtl Number ◽  
Polyatomic Gases ◽  
The Boltzmann Equation ◽  
Fokker Planck

Stochastic solution of the Boltzmann equation for thermal electrons in an attractive Coulombic potential

1969 ◽  
Vol 3 (3) ◽  
pp. 377-385
Author(s):  
M. J. Bell ◽  
M. D. Kostin
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Diffusion Approximation ◽  
Stochastic Method ◽  
Free Electrons ◽  
The Boltzmann Equation ◽  
Stochastic Solution ◽  
Positive Ion ◽  
Fokker Planck

A stochastic method has been employed to investigate the distribution function of free electrons in gases in the field of a positive ion. Stochastic results have been obtained for several pressures and for both large (Langevin) and small ions, and the results have been compared with the solutions of the diffusion approximation and Pitaevskii's Fokker—Planck approximation to the Boltzmann equation.

A Particle Fokker-Planck Algorithm with Multiscale Temporal Discretization for Rarefied and Continuum Gas Flows

2017 ◽  
Vol 22 (2) ◽  
pp. 338-374 ◽  
Author(s):  
Fei Fei ◽  
Zhaohui Liu ◽  
Jun Zhang ◽  
Chuguang Zheng
Keyword(s):  
Boltzmann Equation ◽  
Planck Equation ◽  
Benchmark Problems ◽  
Integration Scheme ◽  
Gas Flows ◽  
Time Step ◽  
Langevin Model ◽  
Temporal Discretization ◽  
The Boltzmann Equation ◽  
Fokker Planck

AbstractFor gas flows with moderate and low Knudsen numbers, pair-wise collisions in the Boltzmann equation can be approximated by the Langevin model corresponding to the Fokker-Planck equation. Using this simplified collision model, particle numerical schemes, e.g. the Fokker-Planck model (FPM) method, can simulate low Knudsen number gas flows more efficient than those based on the Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) method. However, as analyzed in this paper, the transport properties of the FPM method deviate from the physical values as the time step increases, and this problem affects its computational accuracy and efficiency for the simulation of multi-scale flows. Herewe propose a particle Fokker-Planck algorithm with multiscale temporal discretization (MTD-FPM) to overcome the drawbacks of the original FPM method. In the MTD-FPM method, the molecular motion is tracked following the integration scheme of the Langevin model in analogy to the original FPM method. However, to ensure consistent transport coefficients for arbitrary temporal discretization, a time step dependent friction coefficient has been implemented. Several benchmark problems, including Couette, thermal Couette, Poiseuille, and Sod tube flows, are simulated to validate the proposed MTD-FPM method.

scholarly journals A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases

2014 ◽  
Vol 763 ◽  
pp. 24-50 ◽  
Author(s):  
Lei Wu ◽  
Craig White ◽  
Thomas J. Scanlon ◽  
Jason M. Reese ◽  
Yonghao Zhang
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Model ◽  
Transport Coefficients ◽  
Collision Operator ◽  
Elastic Collision ◽  
Distribution Functions ◽  
Parallel Plates ◽  
Polyatomic Gases ◽  
The Boltzmann Equation ◽  
Discrete Velocity Method

AbstractA kinetic model of the Boltzmann equation for non-vibrating polyatomic gases is proposed, based on the Rykov model for diatomic gases. We adopt two velocity distribution functions (VDFs) to describe the system state; inelastic collisions are the same as in the Rykov model, but elastic collisions are modelled by the Boltzmann collision operator (BCO) for monatomic gases, so that the overall kinetic model equation reduces to the Boltzmann equation for monatomic gases in the limit of no translational–rotational energy exchange. The free parameters in the model are determined by comparing the transport coefficients, obtained by a Chapman–Enskog expansion, to values from experiment and kinetic theory. The kinetic model equations are solved numerically using the fast spectral method for elastic collision operators and the discrete velocity method for inelastic ones. The numerical results for normal shock waves and planar Fourier/Couette flows are in good agreement with both conventional direct simulation Monte Carlo (DSMC) results and experimental data. Poiseuille and thermal creep flows of polyatomic gases between two parallel plates are also investigated. Finally, we find that the spectra of both spontaneous and coherent Rayleigh–Brillouin scattering (RBS) compare well with DSMC results, and the computational speed of our model is approximately 300 times faster. Compared to the Rykov model, our model greatly improves prediction accuracy, and reveals the significant influence of molecular models. For coherent RBS, we find that the Rykov model could overpredict the bulk viscosity by a factor of two.

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