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In \cite{NRxx}, we proposed a numerical regularized moment method of arbitrary order (abbreviated as NRxx method) for Boltzmann-BGK equation, which makes numerical simulation using very large number of moments possible. In this paper, we…

Mathematical Physics · Physics 2010-11-30 Zhenning Cai , Ruo Li , Yanli Wang

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

In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) [J. Comput. Phys., Vol. 255, 2013, pp 680-698] originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme…

Numerical Analysis · Mathematics 2016-08-30 Giacomo Dimarco , Raphaël Loubère , Jacek Narski , Thomas Rey

Bhatnagar-Gross-Krook (BGK) collision kernel is employed in the Boltzmann equation to formulate relativistic dissipative hydrodynamics. In this formulation, we find that there remains freedom of choosing a matching condition that affects…

Nuclear Theory · Physics 2024-04-24 Pracheta Singha , Samapan Bhadury , Arghya Mukherjee , Amaresh Jaiswal

A new method for the computation of flows at the micrometer scale is presented. It is based on the recently introduced minimal entropic kinetic models. Both the thermal and isothermal families of minimal models are presented, and the…

Statistical Mechanics · Physics 2007-05-23 S. Ansumali , I. V. Karlin , C. E. Frouzakis , K. B. Boulouchos

Two discretizations of a 9-velocity Boltzmann equation with a BGK collision operator are studied. A Chapman-Enskog expansion of the PDE system predicts that the macroscopic behavior corresponds to the incompressible Navier-Stokes equations…

comp-gas · Physics 2008-02-03 Marc B. Reider , James D. Sterling

A new class of high-order accuracy numerical methods for the BGK model of the Boltzmann equation is presented. The schemes are based on a semi-lagrangian formulation of the BGK equation; time integration is dealt with DIRK (Diagonally…

Numerical Analysis · Mathematics 2014-12-01 M. Groppi , G. Russo , G. Stracquadanio

The gas-kinetic scheme(GKS) is a promising computational fluid dynamics (CFD) method for solving the Navier-Stokes equations. It is based on the analytical solution of the BGK equation, which enables accurate and robust simulations. While…

Fluid Dynamics · Physics 2025-08-12 Yue Zhang , Xing Ji , Kun Xu

Recently, the DSBGK method (note: the original name DS-BGK is changed to DSBGK for simplicity) was proposed based on the BGK equation to reduce the stochastic noise in simulating rarefied gas flows at low velocity, in which the deviation…

Computational Physics · Physics 2012-07-05 Jun Li

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…

Computational Physics · Physics 2015-05-13 Liang Wang , Jianchun Mi , Zhaoli Guo

Gaseous flows under an external force are intrinsically defined by their multi-scale nature due to the large variation of densities along the forcing direction. Devising a numerical method capable of accurately and efficiently solving…

Computational Physics · Physics 2025-07-15 Shuangqing Liu , Zuoxu Li , Yonghao Zhang , Tianbai Xiao

In this paper, a unified gas-kinetic scheme (UGKS) with simplified multi-scale numerical flux is proposed for the thermodynamic non-equilibrium flow simulation involving the excitation of molecular vibrational degrees of freedom in all flow…

Fluid Dynamics · Physics 2023-02-08 Rui Zhang , Sha Liu , Chengwen Zhong , Congshan Zhuo

A recent type of B-spline functions, namely trigonometric cubic B-splines, are adapted to the collocation method for the numerical solutions of the Kuramoto-Sivashinsky equation. Having only first and second order derivatives of the…

Numerical Analysis · Mathematics 2016-12-13 Ozlem Ersoy Hepson

The flow regime of micro flow varies from collisionless regime to hydrodynamic regime according to the Knudsen number. On the kinetic scale, the dynamics of micro flow can be described by the linearized kinetic equation. In the continuum…

Computational Physics · Physics 2020-05-27 Chang Liu , Kun Xu

A well-balanced scheme for a gravitational hydrodynamic system is defined as a scheme which could precisely preserve a hydrostatic isothermal solution. In this paper, we will construct a well-balanced gas-kinetic symplecticity-preserving…

Computational Physics · Physics 2010-12-16 Jun Luo , Kun Xu , Na Liu

Numerically solving the Boltzmann kinetic equations with the small Knudsen number is challenging due to the stiff nonlinear collision term. A class of asymptotic preserving schemes was introduced in [6] to handle this kind of problems. The…

Numerical Analysis · Mathematics 2010-09-20 Francis Filbet , Jingwei Hu , Shi Jin

We consider the neural representation to solve the Boltzmann-BGK equation, especially focusing on the application in microscopic flow problems. A new dimension reduction model of the BGK equation with the flexible auxiliary distribution…

Numerical Analysis · Mathematics 2024-10-30 Pei Zhang , Yanli Wang

Coherent Rayleigh-Brillouin scattering (CRBS) holds great promise for the characterization of gas properties and the investigation of gas kinetic processes. The CRBS spectrum exhibits a strong dependence on the Knudsen number (Kn),…

Fluid Dynamics · Physics 2025-12-23 Xiaozhe Xi , Junzhe Cao , Kun Xu

Kinetic models of polyatomic gas typically account for the internal degrees of freedom at the level of the two-particle distribution function. However, close to the hydrodynamic limit, the internal (rotational) degrees of freedom tend to be…

Fluid Dynamics · Physics 2023-05-24 Praveen Kumar Kolluru , Mohammad Atif , Santosh Ansumali

We consider a kinetic description of a multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In…

Numerical Analysis · Mathematics 2022-11-14 Jeffrey Haack , Cory Hauck , Christian Klingenberg , Marlies Pirner , Sandra Warnecke