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Related papers: BGK model for rarefied gas in a bounded domain

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We consider a multi component mixture of inert gas in the kinetic regime by assuming that the total number of particles of each species remains constant. In this article we shall illustrate our model for the case of two species. To account…

Analysis of PDEs · Mathematics 2018-10-23 Christian Klingenberg , Marlies Pirner , Gabriella Puppo

The spatially homogeneous BGK equation is obtained as the limit if a model of a many particle system, similar to Mark Kac's charicature of the spatially homogeneous Boltzmann equation.

Mathematical Physics · Physics 2020-07-03 Dawan Mustafa , Bernt Wennberg

We continue our investigation of kinetic models of a one-dimensional gas in contact with homogeneous thermal reservoirs at different temperatures. Nonlinear collisional interactions between particles are modeled by a so-called BGK dynamics…

Mathematical Physics · Physics 2019-04-11 Eric Carlen , Raffaele Esposito , Joel Leibowitz , Rossana Marra , Clement Mouhot

We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in $\mathbb R^2$. This solves an open problem. We introduce a new methodology of transforming the single nonlocal…

Analysis of PDEs · Mathematics 2023-12-20 Peter Constantin , Mihaela Ignatova , Quoc-Hung Nguyen

In this paper, we are concerned with the boundary value problem in a slab for the stationary relativistic BGK model of Marle type, which is a relaxation model of the relativistic Boltzmann equation. In the case of fixed inflow boundary…

Analysis of PDEs · Mathematics 2018-01-29 Byung-Hoon Hwang , Seok-Bae Yun

Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially non-trivial velocity distributions. In this paper, moment equations for the bulk velocities,…

Mathematical Physics · Physics 2023-10-20 Evan Habbershaw , Ryan S. Glasby , Jeffrey R. Haack , Cory D. Hauck , Steven M. Wise

In this paper, we propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source)…

Numerical Analysis · Mathematics 2015-05-13 Francis Filbet , S. Jin

The classical problem of steady rarefied gas flow past an infinitely thin circular disk is revisited, with particular emphasis on the gas behavior near the disk edge. The uniform flow is assumed to be perpendicular to the disk surface. An…

Fluid Dynamics · Physics 2026-01-26 Takuma Tomita , Satoshi Taguchi , Tetsuro Tsuji

We present a numerical method for simulating rarefied gases that interact with moving boundaries and rigid bodies. The gas is described by the BGK equation in Lagrangian form and solved using an Arbitrary Lagrangian-Eulerian method, in…

Numerical Analysis · Mathematics 2026-04-28 Klaas Willems , Axel Klar , Giovanni Russo , Giovanni Samaey , Sudarshan Tiwari

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 Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…

Mathematical Physics · Physics 2016-11-30 Marc Briant

Let rarefied gas be confined in an infinite layer with diffusely reflecting boundaries that are isothermal and non-moving. The initial-boundary value problem on the nonlinear Boltzmann equation governing the rarefied gas flow in such…

Analysis of PDEs · Mathematics 2025-08-26 Hongxu Chen , Renjun Duan , Junhao Zhang

Pressure (density) and velocity boundary conditions inside a flow domain are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and new method to specify these conditions are proposed. These conditions are consistent with the…

comp-gas · Physics 2008-02-03 Qisu Zou , Xiaoyi He

This work is devoted to the numerical implementation of the quantum Bhatnagar- Gross-Krook (BGK) model for gas mixtures consisting of classical and quantum particles (fermions, bosons). We consider the model proposed by Bae, Klingenberg,…

Numerical Analysis · Mathematics 2025-02-04 Gi-Chan Bae , Marlies Pirner , Sandra Warnecke

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

The BGK model has been widely used in place of the Boltzmann equation because of the qualitatively satisfactory results it provides at relatively low computational cost. There is, however, a major drawback to the BGK model: The hydrodynamic…

Analysis of PDEs · Mathematics 2015-07-14 Seok-Bae Yun

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

The discrete effect on the boundary condition has been a fundamental topic for the lattice Boltzmann method in simulating heat and mass transfer problems. In previous works based on the halfway anti-bounce-back (ABB) boundary condition for…

Computational Physics · Physics 2020-02-19 Liang Wang , Xuhui Meng , Hao-Chi Wu , Tian-Hu Wang , Gui Lu

A novel discretization approach for the Bhatnager-Gross-Krook (BGK) kinetic equation is proposed. An hierarchy of LB models starting from $D1Q3$ model with increasing number of velocities converging to BGK model is derived. The method…

Computational Physics · Physics 2020-02-19 Oleg Ilyin

We propose two models of the Boltzmann equation (BGK and Fokker-Planck models) for rarefied flows of diatomic gases in vibrational non-equilibrium. These models take into account the discrete repartition of vibration energy modes, which is…

Classical Physics · Physics 2020-07-16 J. Mathiaud , Luc Mieussens