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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 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

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

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

It is challenging to solve the Boltzmann equation accurately due to the extremely high dimensionality and nonlinearity. This paper addresses the idea and implementation of the first flux reconstruction method for high-order Boltzmann…

Computational Physics · Physics 2021-03-19 Tianbai Xiao

A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a BGK collision operator using the lattice Boltzmann method to simulate binary fluid…

Soft Condensed Matter · Physics 2018-05-09 Nicolas Rivas , Stefan Frijters , Ignacio Pagonabarraga , Jens Harting

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple,…

Analysis of PDEs · Mathematics 2012-12-27 Pauline Lafitte , Giovanni Samaey

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

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

This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…

Fluid Dynamics · Physics 2023-12-05 Tarik Dzanic , Luigi Martinelli

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

To simulate non-equilibrium compressible flows, a new discrete Boltzmann model, discrete Ellipsoidal Statistical(ES)-BGK model, is proposed. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number.…

Fluid Dynamics · Physics 2018-03-08 Yudong Zhang , Aiguo Xu , Guangcai Zhang , Zhihua Chen , Pei Wang

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

We consider kinetic and related macroscopic equations on networks. A class of linear kinetic BGK models is considered, where the limit equation for small Knudsen numbers is given by the wave equation. Coupling conditions for the macroscopic…

Numerical Analysis · Mathematics 2025-12-05 Raul Borsche , Tobias Damm , Axel Klar , Yizhou Zhou

Simulating hypersonic flow around a space vehicle is challenging because of the multiscale and nonequilibrium nature inherent in these flows. To effectively deal with such flows, a novel particle particle hybrid scheme combining the…

Fluid Dynamics · Physics 2022-10-19 Fei Fei , Yuan Hu , Patrick Jenny

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

In this paper, a semi-Lagrangian gas-kinetic scheme is developed for smooth flows based on the Bhatnagar-Gross-Krook (BGK) equation. As a finite-volume scheme, the evolution of the average flow variables in a control volume is under the…

Computational Physics · Physics 2014-12-10 Peng Wang , Zhaoli Guo

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

The most rigorous physical description of non-equilibrium gas dynamics is rooted in the numerical solution of the Boltzmann equation. Yet, the large number of degrees of freedom and the wide range of both spatial and temporal scales render…

Computational Physics · Physics 2024-10-25 Anthony Chang , Narendra Singh , Marco Panesi

In this paper we present a parallelization strategy on distributed memory systems for the Fast Kinetic Scheme --- a semi-Lagrangian scheme developed in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] for solving kinetic equations. The…

Numerical Analysis · Mathematics 2017-01-09 Jacek Narski