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Bhatnagar-Gross-Krook (BGK) equation is a relaxation model of the Boltzmann equation which is widely used in place of the Boltzmann equation for the simulation of various kinetic flow problems. In this work, we study the asymptotic…

Analysis of PDEs · Mathematics 2023-01-26 Gi-Chan Bae , Gyounghun Ko , Donghyun Lee , Seok-Bae Yun

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

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

This paper investigates the diffusion limit of a kinetic BGK-type equation, focusing on its relaxation to a nonlinear aggregation-diffusion equation, where the diffusion exhibits a porous-medium-type nonlinearity. Unlike previous studies by…

Analysis of PDEs · Mathematics 2025-04-09 Young-Pil Choi , Jeongho Kim , Oliver Tse

The generalization of the BGK relaxation model to the special relativity setting is revisited here. We deal with several issues related to this relativistic kinetic model which seem to have been overlooked in the previous physical…

Mathematical Physics · Physics 2013-07-12 Abdel Bellouquid , Juan Calvo , Juanjo Nieto , Juan Soler

We propose a BGK-type kinetic model for relativistic reactive gas mixtures. This model serves as a computationally tractable yet physically consistent alternative to the corresponding Boltzmann equation. The relaxation operator is…

Analysis of PDEs · Mathematics 2025-09-03 Seung-Yeon Cho , Byung-Hoon Hwang , Myeong-Su Lee , Seok-Bae Yun

The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is small. In practice, however, Knudsen layers emerge at the…

Numerical Analysis · Mathematics 2019-10-02 Hongxu Chen , Qin Li , Jianfeng Lu

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

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

BGK (Bhatnagar-Gross-Krook) model is a relaxation-type model of the Boltzmann equation, which is popularly used in place of the Boltzmann equation in physics and engineering. In this paper, we address the ill-posedness problem for the BGK…

Analysis of PDEs · Mathematics 2026-03-05 Donghyun Lee , Sungbin Park , Seok-Bae Yun

Unlike the case for classical particles, the literature on BGK type models for relativistic gas mixture is extremely limited. There are a few results %\cite{Kremer,Kremer3,KP} in which such relativistic BGK models for gas mixture are…

Analysis of PDEs · Mathematics 2023-06-09 Byung-Hoon Hwang , Myeong-Su Lee , Seok-Bae Yun

A generalization of the lattice Bhatnagar-Gross-Krook (LBGK) model for the simulation of hydrodynamics is presented, which takes into account the difference and the frame-independence of the relaxation of non-hydrodynamic modes. The present…

Statistical Mechanics · Physics 2011-07-19 I. V. Karlin , D. Lycett-Brown , K. H. Luo

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice…

Statistical Mechanics · Physics 2009-11-11 Mauro Sbragaglia , Sauro Succi

In this paper, we establish the existence of the unique global-in-time classical solutions to the multi-component BGK model suggested in \cite{mixmodel} when the initial data is a small perturbation of global equilibrium. For this, we…

Analysis of PDEs · Mathematics 2022-01-06 Gi-Chan Bae , Christian Klingenberg , Marlies Pirner , Seok-Bae Yun

In this paper we present a new ultra efficient numerical method for solving kinetic equations. In this preliminary work, we present the scheme in the case of the BGK relaxation operator. The scheme, being based on a splitting technique…

Mathematical Physics · Physics 2015-06-04 Giacomo Dimarco , Raphaël Loubere

The mean-state dynamics of free fermions subject to random projective measurements of local occupation number operators is governed by a Lindblad equation with dephasing noise. In the continuum limit, the equation of motion for the…

Statistical Mechanics · Physics 2025-07-29 Michele Coppola

We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation…

Numerical Analysis · Mathematics 2010-10-08 Giacomo Dimarco , Lorenzo Pareschi

In this paper, based on the previous work [B. Shi, Z. Guo, Lattice Boltzmann model for nonlinear convection-diffusion equations, Phys. Rev. E 79 (2009) 016701], we develop a general multiple-relaxation-time (MRT) lattice Boltzmann model for…

Computational Physics · Physics 2016-04-01 Zhenhua Chai , Baochang Shi , Zhaoli Guo

We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we…

Analysis of PDEs · Mathematics 2020-01-15 Liu Liu , Marlies Pirner

Kinetic models for polyatomic gases have two temperatures for the two different types of degrees of freedom, the translational and the internal energy degrees of freedom. Therefore, in the case of BGK models one expects two types of…

Analysis of PDEs · Mathematics 2018-10-23 Marlies Pirner
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