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Related papers: Hypocoercivity for a BGK model for gas mixtures

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We consider a multi component gas mixture with translational and internal energy degrees of freedom assuming that the number of particles of each species remains constant. We will illustrate the derived model in the case of two species, but…

Analysis of PDEs · Mathematics 2018-07-02 Christian Klingenberg , Marlies Pirner , Gabriella Puppo

We propose a BGK model of the quantum Boltzmann equation for gas mixtures. We also provide a sufficient condition that guarantees the existence of equilibrium coefficients so that the model shares the same conservation laws and $H$-theorem…

Analysis of PDEs · Mathematics 2020-07-08 Gi-Chan Bae , Christian Klingenberg , Marlies Pirner , Seok-Bae Yun

In this article, we propose a finite volume discretization of a one dimensional nonlinear reaction kinetic model proposed in [Neumann, Schmeiser, Kint. Rel. Mod. 2016], which describes a 2-species recombination-generation process.…

Numerical Analysis · Mathematics 2024-03-08 Marianne Bessemoulin-Chatard , Tino Laidin , Thomas Rey

This paper presents a unified gas-kinetic wave-particle (UGKWP) method for simulating multiscale binary-species gas mixtures. Benefiting from direct modeling in a discretized space, the UGKWP method enables the automatic decomposition of…

Fluid Dynamics · Physics 2026-05-22 Junzhe Cao , Yufeng Wei , Wenpei Long , Chengwen Zhong , Kun Xu

We present a hybrid Boltzmann-BGK model for inert mixtures, where each kind of binary interaction may be described by a classical Boltzmann integral or by a suitable relaxation-type operator. We allow also the possibility of changing the…

Mathematical Physics · Physics 2025-05-27 Marzia Bisi , Maria Groppi , Giorgio Martalò

In a recent paper [16], the authors proposed a BGK model for relativistic gas mixtures based on the Marle-type approximation, which satisfies the fundamental kinetic properties: non-negativity of distribution functions, conservation laws,…

Analysis of PDEs · Mathematics 2024-04-02 Byung-Hoon Hwang , Myeong-Su Lee

We propose a kinetic relaxation-model to describe a generation-recombination reaction of two species. The decay to equilibrium is studied by two recent methods for proving hypocoercivity of the linearized equations. Exponential decay of…

Analysis of PDEs · Mathematics 2015-03-20 Lukas Neumann , Christian Schmeiser

In this article we focus on kinetic equations for gas mixtures since in applications one often has to deal with mixtures instead of a single gas. In particular we consider an approximation of the Boltzmann equation, the…

Analysis of PDEs · Mathematics 2022-03-30 Marlies Pirner , Sandra Warnecke

In this paper, we consider a BGK-type kinetic model relaxing to the isentropic gas dynamics in the hydrodynamic limit. We introduce a linearization of the equation around the global equilibrium. Then we prove the global existence of…

Analysis of PDEs · Mathematics 2024-02-16 Byung-Hoon Hwang

The multi-scale flow mechanism is crucial for force and heat loaded on near-space and reentry vehicles, the control of spacecraft by thrusters, the propelling and cooling of MEMS, etc. Since the continuum flow and rarefied flow often exist…

Computational Physics · Physics 2021-07-28 Sirui Yang , Sha Liu , Chengwen Zhong , Junzhe Cao , Congshan Zhuo

We consider the global existence and asymptotic behavior of classical solutions to the ellipsoidal BGK model for polyatomic molecules when the initial data starts sufficiently close to a global polyatomic Maxwellian. We observe that the…

Analysis of PDEs · Mathematics 2017-11-08 Seok-Bae Yun

We consider a multi component gas mixture with translational and internal energy degrees of freedom without chemical reactions assuming that the number of particles of each species remains constant. We will illustrate the derived model in…

Analysis of PDEs · Mathematics 2025-01-09 Marlies Pirner

We study the linearized kinetic equation of relaxation model which was proposed by Bhatnagar, Gross and Krook (also called BGK model) and solve the dispersion relation. Using the solution of the dispersion relation, we analyze the…

Solar and Stellar Astrophysics · Physics 2010-10-27 Makoto Takamoto , Shu-ichiro Inutsuka

Consistent BGK models for inert mixtures are compared, first in their kinetic behavior and then versus the hydrodynamic limits that can be derived in different collision-dominated regimes. The comparison is carried out both analytically and…

Mathematical Physics · Physics 2021-02-26 Sebastiano Boscarino , Seung Yeon Cho , Maria Groppi , Giovanni Russo

Kinetic models based on the Bhatnagar-Gross-Krook (BGK) framework provide an efficient alternative to the Boltzmann equation for rarefied gas flows; however, existing formulations for gas mixtures remain limited in representing…

Fluid Dynamics · Physics 2026-04-28 Inchan Kim , Joonbeom Kim , Woonghwi Park , Eunji Jun

We propose a general multi-species Fokker-Planck model. We prove consistency of our model: conservation properties, positivity of all temperatures, H-Theorem and the shape of equilibrium as Maxwell distributions with the same mean velocity…

Analysis of PDEs · Mathematics 2024-09-25 Marlies Pirner

We study the boundary value problem of two stationary BGK-type models - the BGK model for fast chemical reaction and the BGK model for slow chemical reaction - and provide a unified argument to establish the existence and uniqueness of…

Analysis of PDEs · Mathematics 2021-09-01 Doheon Kim , Myeong-Su Lee , Seok-Bae Yun

We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus $(x,v) \in \mathbb{T}^d \times \mathbb{R}^d$ or on the whole space $(x,v) \in…

Analysis of PDEs · Mathematics 2020-11-10 José A. Cañizo , Chuqi Cao , Josephine Evans , Havva Yoldaş

We provide a framework to extend the relative entropy method to a class of diffusive relaxation systems with discrete velocities. The methodology is detailed in the toy case of the 1D Jin-Xin model under the diffusive scaling, and provides…

Analysis of PDEs · Mathematics 2020-01-22 Roberta Bianchini

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…

Analysis of PDEs · Mathematics 2021-10-26 Marlies Pirner