Derivation of a BGK model for mixtures

Brull, Stéphane; Pavan, Vincent; Schneider, Jacques

doi:10.1016/j.euromechflu.2011.12.003

Cited by 64 publications

(102 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Similar to a single gas, the general idea behind how to compute (13) is to reduce the integrals over velocity spaces in (13) into two integrals, which can be separated. When a common temperature for all the gases as well as the for the mixture is assumed, the transformation of the velocities c α and c β to the relative velocity and the velocity of the center of mass splits the integrals over the velocity spaces c α and c β in (13) into two separate integrals-one over the relative velocity and the other over the center of mass velocity, see e.g.…”

Section: General Ideamentioning

confidence: 99%

“…The post-collisional velocities in (13) can be replaced with pre-collisional velocities by using the following relations from the dynamics of binary collisions [15] …”

Section: Full Tensorial Expressionmentioning

confidence: 99%

“…Several authors have attempted to obtain the similar BGK model for gaseous mixtures, see e.g. [7][8][9][10][11][12][13][14], however most of these models either fail to reproduce the correct transport coefficients or do not satisfy some fundamental properties. The recent works [13,14] first consider the transport coefficients computed either by hydrodynamic limit of the Boltzmann equation or by experiments and then construct the BGK model by fitting these coefficients into the model, however both the works are restricted to obtain only correct Fick's and Newton's laws.…”

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

Comparison of relaxation phenomena in binary gas-mixtures of Maxwell molecules and hard spheres

Gupta

Torrilhon

2015

Computers & Mathematics with Applications

View full text Add to dashboard Cite

a b s t r a c tThe strategy for computing the Boltzmann collision integrals for gaseous mixtures is presented and bestowed to compute the fully non-linear Boltzmann collision integrals for hard sphere gas-mixtures. The Boltzmann collision integrals associated with the first 26 moments of each constituent in a gas-mixture are presented. Moreover, the Boltzmann collision integrals are exploited to study the relaxation phenomena of diffusion velocities, stresses and heat fluxes in binary gas-mixtures of Maxwell molecules and hard spheres.

show abstract

Section: General Ideamentioning

confidence: 99%

“…The post-collisional velocities in (13) can be replaced with pre-collisional velocities by using the following relations from the dynamics of binary collisions [15] …”

Section: Full Tensorial Expressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Comparison of relaxation phenomena in binary gas-mixtures of Maxwell molecules and hard spheres

Gupta

Torrilhon

2015

Computers & Mathematics with Applications

View full text Add to dashboard Cite

show abstract

“…Injecting this expression in the continuity equations (26), we obtain multi-species diffusion equations for 1 ≤ j ≤ N − 1,…”

Section: Proofmentioning

confidence: 99%

A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method

Bondesan

Boudin

Grec

2019

Numerical Methods Partial

View full text Add to dashboard Cite

In this article, we consider a multi‐species kinetic model which leads to the Maxwell–Stefan equations under a standard diffusive scaling (small Knudsen and Mach numbers). We propose a suitable numerical scheme which approximates both the solution of the kinetic model in rarefied regime and the one in the diffusion limit. We prove some a priori estimates (mass conservation and nonnegativity) and well‐posedness of the discrete problem. We also present numerical examples where we observe the asymptotic‐preserving behavior of the scheme.

show abstract

“…Consistency like conservation properties (conservation of the number of particles of each species, conservation of total momentum and conservation of total energy), positivity and the H-Theorem is also proven there. Brull, Pavan and Schneider proved in [11] that the model [3] can be derived by an entropy minimization problem. In recent works, there are efforts to extend this type of BGK model for gas mixtures to gas mixtures with chemical reactions, see for example the model of Bisi and Cáceras [9].…”

Section: Introductionmentioning

confidence: 99%

Hypocoercivity for a BGK model for gas mixtures

Liu

Pirner

2019

Journal of Differential Equations

View full text Add to dashboard Cite

We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we can prove exponential relaxation to equilibrium with explicit rates. Our strategy is based on the entropy and spectral methods adapting Lyapunov's direct method as presented in [1] for the one species linearized BGK model. In comparison to the one species case, we start with two partial differential equations, one for each species. These equations are coupled due to interspecies interactions, which requires additional estimates on these interspecies terms. Nonlinear BGK model for gas mixturesWe want to consider the BGK model for gas mixtures described in [21]. For the convenience of the reader, we want to briefly repeat it here. For more details, see [21]. We consider the position spacẽ T d := L 2Π T d , the d-dimensional torus of side length L. Then, we consider the following BGK

show abstract

Derivation of a BGK model for mixtures

Cited by 64 publications

References 23 publications

Comparison of relaxation phenomena in binary gas-mixtures of Maxwell molecules and hard spheres

Comparison of relaxation phenomena in binary gas-mixtures of Maxwell molecules and hard spheres

A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method

Hypocoercivity for a BGK model for gas mixtures

Contact Info

Product

Resources

About