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

Gupta, V. B.; Torrilhon, Manuel

doi:10.1016/j.camwa.2015.04.028

Cited by 16 publications

(6 citation statements)

References 28 publications

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“…For the above one-dimensional problem, the relevant boundary conditions associated with the 2×G13 equations are conditions (27)-(30) for each constituent while those associated with the 2×G26 equations are conditions (27), (28) and (31)-(33) for each constituent. Note that boundary conditions (29) and (31) for the problem under consideration just imply that the slip velocity vanishes, i.e, V = 0, and the other boundary conditions-for the problem under consideration-in linear-dimensionless form are as follows. Boundary conditions (27) and 28read…”

Section: Linear-dimensionless Boundary Conditionsmentioning

confidence: 99%

“…Recently, the method has also been extended to single-component rarefied granular gases of hard spheres [25][26][27]. It is worth to note that the computation of full nonlinear production terms-the terms arising from the Boltzmann collision operator-associated with the moment equations derived in these works is not easy, and the present authors have also developed an automated way to compute them using computer algebra software Mathematica R , see [23,[28][29][30] for its details and [31] for the source code.…”

Section: Introductionmentioning

confidence: 99%

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Heat flux in binary gas mixtures confined between two parallel plates via moment equations

Gupta

Torrilhon

2019

31st International Symposium on Rarefied Gas Dynamics: Rgd31

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The steady heat transfer problem in two-component gas mixtures of noble (monatomic) gases confined between two infinite parallel plates having different temperatures has been investigated with the Grad 13-and 26-moment equations for Maxwell molecules as well as for hard-sphere molecules. The heat flux normal to the plates is computed via the aforementioned models for three gas mixtures, namely neon-argon, helium-argon and helium-xenon, for different mole fraction ratios. The heat flux profiles computed through the Grad moment equations in this work turn out to be in reasonably good agreement with those obtained through the discrete velocity method in [1].

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Section: Linear-dimensionless Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Heat flux in binary gas mixtures confined between two parallel plates via moment equations

Gupta

Torrilhon

2019

31st International Symposium on Rarefied Gas Dynamics: Rgd31

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“…The details of the computation can be found in Gupta & Torrilhon (2012) and the source code for the computation is provided as supplementary material with the present paper. Interested readers are also referred to Gupta & Torrilhon (2015b); Gupta (2015) for deriving the higher-order moment equations for monatomic gas mixtures and to Gupta & Torrilhon (2015a); Gupta (2015) for learning the computation of their associated production terms, which might be useful in developing higher-order moment theories for granular gas mixtures. For the sake of completeness, we provide the production terms associated with the G26 equations (eqs.…”

Section: Grad 26-moment Closurementioning

confidence: 99%

Higher-order moment theories for dilute granular gases of smooth hard spheres

2017

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Grad's method of moments is employed to develop higher-order Grad moment equations-up to first 26-moments-for dilute granular gases within the framework of the (inelastic) Boltzmann equation. The homogeneous cooling state of a freely cooling granular gas is investigated with the Grad 26-moment equations in a semi-linearized setting and it is shown that the granular temperature in the homogeneous cooling state still decays according to Haff's law while the other higher-order moments decay on a faster time scale. The nonlinear terms of fully contracted fourth moment are also considered and, by exploiting the stability analysis of fixed points, it is shown that these nonlinear terms have negligible effect on Haff's law. Furthermore, an even larger Grad moment system which includes the fully contracted sixth moment is also scrutinized and the stability analysis of fixed points is again exploited to conclude that even the inclusion of scalar sixth order moment into the Grad moment system has negligible effect on Haff's law. The constitutive relations for the stress and heat flux (i.e., the Navier-Stokes and Fourier relations) are derived through the Grad 26-moment equations and compared with those obtained via CE expansion and via computer simulations. The linear stability of the homogeneous cooling state is analyzed through the Grad 26-moment system and various sub-systems by decomposing them into longitudinal and transverse systems. It is found that one eigenmode in both longitudinal and transverse systems in the case of inelastic gases is unstable. By comparing the eigenmodes from various theories, it is established that the 13-moment eigenmode theory predicts that the unstable heat mode of the longitudinal system remains unstable for all wavenumbers below a certain coefficient of restitution while any other higher-order moment theory shows that this mode becomes stable above some critical wavenumber for all values of the coefficient of restitution. In particular, the Grad 26-moment theory leads to a smooth profile for the critical wavenumber in contrast to the other considered theories. Furthermore, the critical system size obtained through the Grad 26-moment and existing theories are also in excellent agreement.

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“…It is well-known that the numerical methods for multi-species Boltzmann equations are computationally expensive (see for instance [30] and the references therein). On the other hand, BGK approximations are not able to reproduce peculiar nonlinear effects, especially in the evolution of high order moments in mixtures with heavy and light components [29]. This is also due to the fact that BGK operators do not include all the details of the different intermolecular potentials [50].…”

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confidence: 98%

A mixed Boltzmann–BGK model for inert gas mixtures

Bisi,

Groppi,

Lucchin

et al. 2024

KRM

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We propose a mixed Boltzmann-BGK model for mixtures of monatomic gases, where some kinds of collisions are described by bi-species Boltzmann operators and the others by the binary BGK terms given in [Bobylev et al., Kinetic and Related Models 11 (2018)], that is the relaxation model for mixtures with the closest structure to the Boltzmann one. At first, we assume that collisions occurring within the same species (intra-species) are modelled by Boltzmann operators, while interactions between different constituents (inter-species) are described by BGK terms. This option allows us to rigorously derive hydrodynamic equations not only in the classical collision dominated regime, but also in situations with intra-species collisions playing the dominant role (as in mixtures with very disparate particle masses). Then, we present a general form of this mixed Boltzmann-BGK model, characterized by further parameters allowing us to select which binary interactions have to be described by Boltzmann integrals or by BGK operators. We prove that this model preserves conservations of global momentum and energy, positivity of all temperatures and the validity of Boltzmann H-theorem, allowing us to conclude that the unique admissible equilibrium state is the expected Maxwellian distribution with all species sharing a common mean velocity and a common temperature.

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

Cited by 16 publications

References 28 publications

Heat flux in binary gas mixtures confined between two parallel plates via moment equations

Heat flux in binary gas mixtures confined between two parallel plates via moment equations

Higher-order moment theories for dilute granular gases of smooth hard spheres

A mixed Boltzmann–BGK model for inert gas mixtures

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