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This paper is concerned with the analysis of polyatomic gases within the framework of kinetic theory. Internal degrees of freedom are modeled using a single continuous variable corresponding to the molecular internal energy. Non-equilibrium…

Mathematical Physics · Physics 2016-11-15 Milana Pavić-Čolić , Damir Madjarević , Srboljub Simić

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

The non-equilibrium gas dynamics is described by the Boltzmann equation, which can be solved numerically through the deterministic and stochastic methods. Due to the complicated collision term of the Boltzmann equation, many kinetic…

Computational Physics · Physics 2021-02-03 Xiaocong Xu , Yipei Chen , Kun Xu

We consider a class of nonlinear, spatially inhomogeneous kinetic equations of BGK-type with density dependent collision rates. These equations share the same superlinearity as the Boltzmann equation, and fall into the class of run and…

Analysis of PDEs · Mathematics 2026-01-29 Josephine Evans , Daniel Morris , Havva Yoldaş

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

A kinetic model called the $\nu$-model is proposed to replace the complicated Boltzmann collision operator in the simulation of rarefied flows of monatomic gas. The model follows the relaxation-time approximation, but the collision…

Computational Physics · Physics 2022-01-26 Yuan RuiFeng , Wu Lei

In this work, we propose a class of high order semi-Lagrangian scheme for a general consistent BGK model for inert gas mixtures. The proposed scheme not only fulfills indifferentiability principle, but also asymptotic preserving property,…

Numerical Analysis · Mathematics 2020-12-07 Seung Yeon Cho , Sebastiano Boscarino , Maria Groppi , Giovanni Russo

Boltzmann equation requires some alternative simpler kinetic model like BGK to replace the collision term. Such a kinetic model which replaces the Boltzmann collision integral should preserve the basic properties and characteristics of the…

Fluid Dynamics · Physics 2013-12-31 Ajit Kumar Mahendra , Ram Kumar Singh

This work is devoted to the numerical simulation of the \BGK equation for two species in the fluid limit using a particle method. Thus, we are interested in a gas mixture consisting of two species without chemical reactions assuming that…

Analysis of PDEs · Mathematics 2018-10-23 A. Crestetto , C. Klingenberg , M. Pirner

The one-dimensional kinetic equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and frequency of collisions affine depending on the module of molecular velocity is constructed. Laws of preservation of number of…

Mathematical Physics · Physics 2014-03-11 A. L. Bugrimov , A. V. Latyshev , A. A. Yushkanov

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 apply the collision-based hybrid introduced in \cite{hauck} to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator.…

Numerical Analysis · Mathematics 2023-06-21 Minwoo Shin , Cory D. Hauck , Ryan G. McClarren

We propose a BGK-type kinetic model for a binary gas mixture, designed to serve as a kinetic formulation of compressible two-phase fluid dynamics. The model features species-dependent adiabatic exponents, and the relaxation operator is…

Analysis of PDEs · Mathematics 2025-06-25 Seung Yeon Cho , Young-Pil Choi , Byung-Hoon Hwang , Sihyun Song

We study the Bathnagar-Gross-Krook (BGK) equation in a smooth bounded domain featuring a diffusive reflection boundary condition with general collision frequency. We prove that the BGK equation admits a unique global solution with an…

Analysis of PDEs · Mathematics 2026-01-09 Hongxu Chen , Christian Klingenberg , Marlies Pirner

The Bhatnagar-Gross-Krook (BGK) single-relaxation-time collision model for the Boltzmann equation serves as the foundation of the lattice BGK (LBGK) method developed in recent years. The description of the collision as a uniform relaxation…

Numerical Analysis · Mathematics 2021-10-04 Xiaowen Shan , Yangyang Shi , Xuhui Li

The Boltzmann kinetic equation for low-density granular suspensions under simple shear flow is considered to determine the velocity moments through the fourth degree. The influence of the interstitial gas on solid particles is modeled by a…

Statistical Mechanics · Physics 2019-01-09 Rubén Gómez González , Vicente Garzó

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 address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…

Statistical Mechanics · Physics 2009-10-31 A. Puglisi , V. Loreto , U. Marini Bettolo Marconi , A. Vulpiani

A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…

General Relativity and Quantum Cosmology · Physics 2026-04-13 Philip Semrén , Michael Bradley , João M. S. Oliveira , M. Piedade Machado Ramos

This paper establishes the global well-posedness of the multi-species Boltzmann equation with large-amplitude initial data in the periodic domain $\mathbb{T}^3$. In contrast to the single-species case, the multi-species mixture model lacks…

Analysis of PDEs · Mathematics 2026-05-12 Gyounghun Ko , Myeong-Su Lee , Sung-Jun Son