BGK and Fokker-Planck Models of the Boltzmann Equation for Gases with Discrete Levels of Vibrational Energy

Mathiaud, Julien; Mieussens, Luc

doi:10.1007/s10955-020-02490-7

Cited by 16 publications

(12 citation statements)

References 21 publications

(49 reference statements)

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“…where Λ(δ) = 1/Γ( δ 2 ), with Γ the usual gamma function. This Maxwellian distribution can be used to define the BGK approximation Mathiaud & Mieussens (2020), where…”

Section: Construction Of the Modelmentioning

confidence: 99%

An ES-BGK model for diatomic gases with correct relaxation rates for internal energies

Mathiaud,

Mieussens,

Pfeiffer

2022

Preprint

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We propose a new ES-BGK model for diatomic gases which allows for translational-rotational and translational-vibrational energy exchanges, as given by Landau-Teller and Jeans relaxation equations. This model is consistent with the general definition of the vibrational and rotational collision numbers that are also commonly used in DSMC solvers. It is proved to satisfy the H-theorem and to give the correct transport coefficients, up to the volume viscosity.

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“…where Λ(δ) = 1/Γ( δ 2 ), with Γ the usual gamma function. This Maxwellian distribution can be used to define the BGK approximation Mathiaud & Mieussens (2020), where…”

Section: Construction Of the Modelmentioning

confidence: 99%

An ES-BGK model for diatomic gases with correct relaxation rates for internal energies

Mathiaud,

Mieussens,

Pfeiffer

2022

Preprint

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“…Here we define the distribution function f (3) = f (3) (x, v, t, I, i) where I ∈ R + 0 describes the internal energy in a continuous way, whereas i denotes the ith vibrational energy level of the corresponding vibrational energy iRhν kB (h is the Planck constant, R the fundamental gas constant, while ν is the fundamental vibrational frequency of the molecule). This is done for example in [35].…”

Section: 22mentioning

confidence: 99%

A review on BGK models for gas mixtures of mono and polyatomic molecules

Pirner¹

2021

Preprint

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We consider the socalled Bathnagar-Gross-Krook (BGK) model, an approximation of the Boltzmann equation, describing the time evolution of a single momoatomic rarefied gas and satisfying the same two main properties (conservation properties and entropy inequality). However, in practical applications one often has to deal with twoo additional physical issues. First, a gas often does not consist of only one species, but it consists of mixture a mixture of different species. Second, the particles can store energy not only in translational degrees of freedom but also in internal degrees of freedom like rotations or vibrations (polyatomic molecules). Therefore, here, we will present recent BGK models for gas mixtures for mono-and polyatomic particles and the existing mathematical theory for these models.

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“…This is the main motivation for the present work; indeed, we would like to merge the existing discrete and continuous energy models in a general (abstract) framework, in order to combine their strength and obtain a full description of both rotation and vibration. Some attempts to distinguish vibrational from rotational energy have recently been performed in [30,31] at BGK or Fokker-Planck level, or in the frame of Extended Thermodynamics introducing two continuous energy variables [32].…”

Section: Introductionmentioning

confidence: 99%

A general framework for the kinetic modeling of polyatomic gases

Borsoni,

Bisi,

Groppi

2021

Preprint

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A general framework for the kinetic modelling of non-relativistic polyatomic gases is proposed, where each particle is characterized both by its velocity and by its internal state, and the Boltzmann collision operator involves suitably weighted integrals over the space of internal energies. The description of the internal structure of a molecule is kept highly general, and this allows classical and semi-classical models, such as the monoatomic gas description, the continuous internal energy structure, and the description with discrete internal energy levels, to fit our framework. We prove the H-Theorem for the proposed kinetic equation of Boltzmann type in this general setting, and characterize the equilibrium Maxwellian distribution and the thermodynamic number of degrees of freedom. Euler equations are derived, as zero-order approximation in a suitable asymptotic expansion. In addition, within this general framework it is possible to build up new models, highly desirable for physical applications, where rotation and vibration are precisely described. Examples of models for the Hydrogen Fluoride gas are presented.

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BGK and Fokker-Planck Models of the Boltzmann Equation for Gases with Discrete Levels of Vibrational Energy

Cited by 16 publications

References 21 publications

An ES-BGK model for diatomic gases with correct relaxation rates for internal energies

An ES-BGK model for diatomic gases with correct relaxation rates for internal energies

A review on BGK models for gas mixtures of mono and polyatomic molecules

A general framework for the kinetic modeling of polyatomic gases

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