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A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal…

Statistical Mechanics · Physics 2009-11-10 James W. Dufty , Aparna Baskaran , Lorena Zogaib

We show that the spatially homogeneous Boltzmann equation evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures which takes the collision process into account. This gradient…

Analysis of PDEs · Mathematics 2023-06-14 Matthias Erbar

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…

We demonstrate the implementation of a hybrid OpenMP and MPI parallelization of a conservative spectral method for the Boltzmann equation originally developed by Gamba and Tharkabhushaman. We perform a scaling analysis to demonstrate that…

Numerical Analysis · Mathematics 2013-01-18 Jeffrey Haack

In this paper, we propose a numerical regularized moment method to solve the Boltzmann equation with ES-BGK collision term to simulate polyatomic gas flows. This method is an extension to the polyatomic case of the method proposed in [9],…

Mathematical Physics · Physics 2012-02-17 Zhenning Cai , Ruo Li

We reduce the eight-dimensional weak form of the bilinear Boltzmann collision operator to a five-dimensional kinematic core by rigidly rotating the laboratory frame to align with the colliding pair and integrating over the $\mathrm{SO}(3)$…

Numerical Analysis · Mathematics 2026-05-28 René R. Hiemstra , Torsten Keßler , Michael R. A. Abdelmalik

For the spatially homogeneous Boltzmann equation with hard po- tentials and Grad's cutoff (e.g. hard spheres), we give quantitative estimates of exponential convergence to equilibrium, and we show that the rate of exponential decay is…

Analysis of PDEs · Mathematics 2016-08-16 Clément Mouhot

We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral…

Statistical Mechanics · Physics 2009-11-10 Fabrizio Capuani , Ignacio Pagonabarraga , Daan Frenkel

Recently, a new class of semi-Lagrangian methods for the BGK model of the Boltzmann equation has been introduced [8, 17, 18]. These methods work in a satisfactory way either in rarefied or fluid regime. Moreover, because of the…

Analysis of PDEs · Mathematics 2010-07-19 Giovanni Russo , Pietro Santagati , Seok-Bae Yun

The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and…

Plasma Physics · Physics 2023-08-09 George J. Wilkie , Torsten Keßler , Sergej Rjasanow

We study the acceleration of steady-state computation for microflow, which is modeled by the high-order moment models derived recently from the steady-state Boltzmann equation with BGK-type collision term. By using the lower-order model…

Numerical Analysis · Mathematics 2016-11-23 Zhicheng Hu , Ruo Li , Zhonghua Qiao

The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…

Plasma Physics · Physics 2024-02-27 Nils W. Schween , Brian Reville

A new form of the model collision operator for a Boltzmann gas of hard spheres and Coulomb plasma is derived. One-component and many-component systems are considered. The collision operator proposed takes properly into account the…

Statistical Mechanics · Physics 2014-09-23 Viacheslav V. Belyi

This paper presents a numerical approximation technique for the Boltzmann equation based on a moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure…

Computational Physics · Physics 2016-02-04 M. R. A. Abdelmalik , E. H. van Brummelen

A general framework for constructing discrete Boltzmann model for non-equilibrium flows based on the Shakhov model is presented. The Hermite polynomial expansion and a set of discrete velocity with isotropy are adopted to solve the kinetic…

Fluid Dynamics · Physics 2019-03-27 Yudong Zhang , Aiguo Xu , Guangcai Zhang , Zhihua Chen , Pei Wang

Building upon the Integer Lattice Gas Automata framework of Blommel \textit{et al.} \cite{PhysRevE.97.023310}, we introduce a simplified, fluctuation-free variant. This approach relies on floating-point numbers and closely mirrors the…

This paper presents a general framework for constructing reduced models that approximate the Boltzmann equation with arbitrary orders of accuracy in terms of the Knudsen number $\mathit{Kn}$, applicable to general collision models in…

Mathematical Physics · Physics 2025-05-19 Zhenning Cai , Ruo Li , Yixiao Lu , Yanli Wang

We are interested in solving the Boltzmann equation of chemically reacting rarefied gas flows using the Grad's-14 moment method. We first propose a novel mathematical model that describes the collision dynamics of chemically reacting hard…

Computational Physics · Physics 2021-04-28 Neeraj Sarna , Georgii Oblapenko , Manuel Torrilhon

The quantitative information on the spectral gaps for the linearized Boltzmann operator is of primary importance on justifying the Boltzmann model and study of relaxation to equilibrium. This work, for the first time, provides numerical…

Mathematical Physics · Physics 2018-07-27 Chenglong Zhang , Irene M. Gamba

We give an explicit description of the spectral closure for the three-dimensional linear Boltzmann-BGK equation in terms of the macroscopic fields, density, flow velocity and temperature. This results in a new linear fluid dynamics model…

Analysis of PDEs · Mathematics 2023-06-13 Florian Kogelbauer , Ilya Karlin
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