Statistical moments and integrability properties of monatomic gas mixtures with long range interactions

Alonso, Ricardo; Orf, Hajer

doi:10.48550/arxiv.2204.09160

Cited by 1 publication

(2 citation statements)

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“…depending on fictitious quantities n sr , u sr and T sr . Such auxiliary fields are 5 N 2 disposable parameters that can be expressed in terms of species densities, velocities and temperatures in order to make the BGK model ( 10) a good approximation of the Boltzmann model (1). A requirement to be fulfilled by any kinetic model for inert gas mixtures is the conservation of species number densities, global momentum and kinetic energy; this provides N + 4 constraints on the fictitious quantities.…”

Section: 2mentioning

confidence: 99%

“…The kinetic theory approach to gas mixtures has gained much interest in last decades, and the Boltzmann description has also been generalized to reacting mixtures [46] and to polyatomic constituents [22,25,27]. As concerns inert mixtures of monatomic gases, Boltzmann equations for species distribution functions are well known in the literature [18,19], but the investigation of their mathematical properties is still in progress (see for instance some recent results in [1,15,24]) as well as the construction of effective numerical schemes for them [12,20,51,53]. Since these equations are quite awkward to deal with, several approximations have been proposed, mainly of BGK type, generalizing the relaxation model presented in [3] for a single gas.…”

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confidence: 99%

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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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Section: 2mentioning

confidence: 99%