A Kinetic Model for Gas Mixtures Based on a Fokker-Planck Equation

Gorji, M. Hossein; Jenny, Patrick

doi:10.1088/1742-6596/362/1/012042

Cited by 29 publications

(26 citation statements)

References 5 publications

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“…The FP method for RGD was also generalized for mixtures and polyatomic gas, and a variance reduction scheme was devised to cope with the stochastic noise, which is, in particular, problematic in low Mach number flow simulations. 24,25,27 The most important development, however, is the combination of the FP method with DSMC. 30,31,42 The resulting FPDSMC method offers unique advantages in simulating gas flows where continuum and rarefied regions coexist.…”

Section: Physics Of Fluidsmentioning

confidence: 99%

“…However, their modification requires evaluation of the temperature gradient and hence does not reproduce correct relaxation rates of heat fluxes in a space-independent scenario. Later, the FP model was extended for mixtures 22 and polyatomic gas, [23][24][25][26] and a noise reduction scheme for low Mach numbers was devised. 27 In this context also, an improved wall kernel was developed, 19 which accounts for internal energy modes.…”

Section: Introductionmentioning

confidence: 99%

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Controlling the bias error of Fokker-Planck methods for rarefied gas dynamics simulations

2019

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Direct simulation Monte-Carlo (DSMC) is the most established method for rarefied gas flow simulations. It is valid from continuum to near vacuum, but in cases involving small Knudsen numbers (Kn), it suffers from high computational cost. The Fokker-Planck (FP) method, on the other hand, is almost as accurate as DSMC for small to moderate Kn, but it does not have the computational drawback of DSMC, if Kn is small [P. Jenny, M. Torrilhon, and S. Heinz, “A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion,” J. Comput. Phys. 229, 1077–1098 (2010) and H. Gorji, M. Torrilhon, and P. Jenny, “Fokker–Planck model for computational studies of monatomic rarefied gas flows,” J. Fluid Mech. 680, 574–601 (2011)]. Especially attractive is the combination of the two approaches leading to the FP-DSMC method. Opposed to other hybrid methods, e.g., coupled DSMC/Navier-Stokes solvers, it is relatively straightforward to couple DSMC with the FP method since both are based on particle solution algorithms sharing the same data structure and having similar components. Regarding the numerical accuracy of such particle methods, one has to distinguish between spatial truncation errors, time stepping errors, statistical errors and bias errors. In this paper, the bias error of the FP method is analyzed in detail, and it is shown how it can be reduced without increasing the particle number to an exorbitant level. The effectiveness of the discussed bias error reduction scheme is demonstrated for uniform shear flow, for which an analytical reference solution was derived.

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Section: Physics Of Fluidsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Controlling the bias error of Fokker-Planck methods for rarefied gas dynamics simulations

2019

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“…Very recently, in a series of paper [13,12,10,11], Jenny et al proposed a very different and innovative approach: they proposed to use a different model equation known as the Fokker-Planck model to design a rarefied flow solver. In this model, the collisions are taken into account by a diffusion process in the velocity space.…”

Section: Introductionmentioning

confidence: 99%

“…However, this Fokker-Planck model is parametrized by a single parameter, like the BGK model, and hence cannot give the correct transport coefficients in near equilibrium regimes: this is often stated by showing that the Prandtl number-which is the ratio between the viscosity to the heat transfer coefficient-has an incorrect value. The authors have proposed a modified model that allow to fit the correct value of the Prandtl number [12], and then have extended it to more complex flows (multi-species [10] and diatomic [11]). However, even if the results obtained with this approach seem very accurate, it is not clear that these models still satisfy the H-theorem.…”

Section: Introductionmentioning

confidence: 99%

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

Mathiaud

Mieussens

2017

J Stat Phys

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We propose an extension of the Fokker-Planck model of the Boltzmann equation to get a correct Prandtl number in the Compressible Navier-Stokes asymptotics for polyatomic gases. This is obtained by replacing the diffusion coefficient (which is the equilibrium temperature) by a non diagonal temperature tensor, like the Ellipsoidal-Statistical model is obtained from the Bathnagar-Gross-Krook model of the Boltzmann equation, and by adding a diffusion term for the internal energy. Our model is proved to satisfy the properties of conservation and a H-theorem. A Chapman-Enskog analysis shows how to compute the transport coefficients of our model. Some numerical tests are performed to illustrate that a correct Prandtl number can be obtained.

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“…Two of them (BGK and ES-BGK) also satisfy the important entropy dissipation property (the so-called "H-theorem") [2]. Very recently, in a series of paper [13,12,10,11], Jenny et al proposed a very different and innovative approach: they proposed to use a different model equation known as the Fokker-Planck model to design a rarefied flow solver. In this model, the collisions are taken into account by a diffusion process in the velocity space.…”

mentioning

confidence: 99%