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In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. In order to avoid time step restrictions coming from convection term and small Knudsen number, we combine a semi-Lagrangian approach for the…

Numerical Analysis · Mathematics 2020-03-03 Sebastiano Boscarino , Seung-Yeon Cho , Giovanni Russo , Seok-Bae Yun

In this paper, we propose a high-order domain decomposition method for the ES-BGK model of the Boltzmann equation, which dynamically detects regions of equilibrium and non-equilibrium. Our implementation automatically switches between Euler…

Numerical Analysis · Mathematics 2025-12-04 Domenico Caparello , Tommaso Tenna

This paper presents second-order accurate genuine BGK (Bhatnagar-Gross-Krook) schemes in the framework of finite volume method for the ultra-relativistic flows. Different from the existing kinetic flux-vector splitting (KFVS) or BGK-type…

Numerical Analysis · Mathematics 2017-09-13 Yaping Chen , Yangyu Kuang , Huazhong Tang

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

This short note presents an extension of the hybrid, model-adaptation method introduced in [T.~Laidin, \textit{arXiv 2202.03696}, 2022] for linear collisional kinetic equations in a diffusive scaling to the nonlinear mean-field…

Numerical Analysis · Mathematics 2023-03-16 Tino Laidin , Thomas Rey

In this work, we present a hierarchical domain decomposition method for the multi-scale Boltzmann equation based on moment realizability matrices, a concept introduced by Levermore, Morokoff, and Nadiga in \cite{lev-mor-nad-1998}. This…

Numerical Analysis · Mathematics 2025-05-07 Domenico Caparello , Lorenzo Pareschi , Thomas Rey

This article extends a recently introduced kinetic closure of turbulence by developing its theoretical framework, operational realizations, and validation. In contrast with filtered Navier--Stokes formulations, filtering the Boltzmann…

Fluid Dynamics · Physics 2026-05-20 Francesco Marson , Orestis Malaspinas

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…

Fluid Dynamics · Physics 2023-07-05 Hiroshi Otomo

We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the…

Quantum Physics · Physics 2023-04-13 Wael Itani , Katepalli R. Sreenivasan , Sauro Succi

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

In dilute gas kinetic theory, model collision dynamics such as Bhatnagar-Gross-Krook (BGK) model is often used to get a better insight and numerical modelling. BGK model and its variants assume that highly nonlinear collision term can be…

Statistical Mechanics · Physics 2020-08-26 Samarth Agrawal , S. K. Singh , Santosh Ansumali

The lattice Boltzmann (LB) method intrinsically links to the Boltzmann equation with the Bhatnagar-Gross-Krook collision operator; however, it has been questioned to be able to simulate noncontinuum bounded gas flows at the micro and…

Computational Physics · Physics 2022-08-24 Yong Shi

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 paper, we propose an efficient, high order accurate and asymptotic-preserving (AP) semi-Lagrangian (SL) method for the BGK model with constant or spatially dependent Knudsen number. The spatial discretization is performed by a mass…

Numerical Analysis · Mathematics 2021-05-07 Mingchang Ding , Jing-Mei Qiu , Ruiwen Shu

We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary…

Numerical Analysis · Mathematics 2015-09-14 Qin Li , Jianfeng Lu , Weiran Sun

In this paper, we first extend the micro-macro decomposition method for multiscale kinetic equations from the BGK model to general collisional kinetic equations, including the Boltzmann and the Fokker-Planck Landau equations. The main idea…

Numerical Analysis · Mathematics 2019-02-20 Irene M. Gamba , Shi Jin , Liu Liu

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

We introduce numerical solvers for the steady-state Boltzmann equation based on the symmetric Gauss-Seidel (SGS) method. Due to the quadratic collision operator in the Boltzmann equation, the SGS method requires solving a nonlinear system…

Computational Physics · Physics 2023-11-27 Tianai Yin , Zhenning Cai , Yanli Wang

We propose a well-posed Maxwell-type boundary condition for the linear moment system in half-space. As a reduction of the Boltzmann equation, the moment equations are available to model Knudsen layers near a solid wall, where proper…

Analysis of PDEs · Mathematics 2023-01-31 Ruo Li , Yichen Yang

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…

Numerical Analysis · Mathematics 2024-10-18 Ying Chen , Zhenhua Chai , Baochang Shi