Related papers: Large amplitude problem of BGK model: Relaxation t…
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…
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…
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…
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…
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…
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…
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…
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…
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…
The Boltzmann equation describes the detailed microscopic behaviour of a dilute gas, and represents the basis of the kinetic theory of gases. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a…
The Bhatnagar-Gross-Krook (BGK) Boltzmann equation with the Maxwellian-Boltzmann-type equilibrium state leads to the set of thermo-hydrodynamic equations such as the continuity, the Navier-Stokes, and the heat-transfer equations in the…
In this work, we first develop a unified Bhatnagar-Gross-Krook lattice Boltzmann (BGK-LB) model for the $d$($d\geq 1$)-dimensional linear hyperbolic equation (L-HE), where the natural moments and the D$d$Q$(2d^2+1)$ [($2d^2+1$) discrete…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…
A thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single…
The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation allows for efficient flow simulations, especially in the transition regime between continuum and high rarefaction. However, ensuring efficient performances for multiscale…
We study the stability and sensitivity of an absorbing layer for the Boltzmann equation by examining the Bhatnagar-Gross-Krook (BGK) approximation and using the perfectly matched layer (PML) technique. To ensure stability, we discard some…
The Boltzmann collision operator for a dilute granular gas of inelastic rough hard spheres is much more intricate than its counterpart for inelastic smooth spheres. Now the one-body distribution function depends not only on the…
Solving the Bhatnagar-Gross-Krook (BGK) equation with a stochastic particle approach enables efficient and flexible simulations of flows in the transition regime, between continuum and free molecular flow. However, the usual first-order…
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…
The lattice Bhatnagar-Gross-Krook (LBGK) model has become the most popular one in the lattice Boltzmann method for simulating the convection heat transfer in porous media. However, the LBGK model generally suffers from numerical instability…