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A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is…

Statistical Mechanics · Physics 2022-01-12 Takashi Arima , Maria Cristina Carrisi , Sebastiano Pennisi , Tommaso Ruggeri

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…

Fluid Dynamics · Physics 2024-12-02 Marcel Pfeiffer , Félix Garmirian , Tobias Ott

We present a more refined version of rational extended thermodynamics of rarefied polyatomic gases in which molecular rotational and vibrational relaxation processes are treated individually. In this case we need a triple hierarchy of the…

Statistical Mechanics · Physics 2017-10-25 Takashi Arima , Tommaso Ruggeri , Masaru Sugiyama

In this paper we present a fully deterministic method for the numerical solution to the Boltzmann equation of rarefied gas dynamics in a bounded domain for multi-scale problems. Periodic, specular reflection and diffusive boundary…

Numerical Analysis · Mathematics 2011-06-07 Francis Filbet

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

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

In this paper we present a numerical method for the Boltzmann equation. It is a spectral discretization in the velocity and a discontinuous Galerkin discretization in physical space. To obtain uniform approximation properties in the mach…

Numerical Analysis · Mathematics 2019-03-06 Gerhard Kitzler , Joachim Schöberl

We study the structure of a shock wave for a two-, three- and four-component gas mixture on the basis of numerical solution of the Boltzmann equation for the model of hard sphere molecules. For the evaluation of collision integrals we use…

Fluid Dynamics · Physics 2014-03-14 A. A. Raines

In this paper we present a numerical scheme to simulate a moving rigid body with arbitrary shape suspended in a rarefied gas. The rarefied gas is simulated by solving the Boltzmann equation using a DSMC particle method. The motion of the…

Computational Physics · Physics 2015-06-22 Samir Shrestha , Sudarshan Tiwari , Axel Klar , Steffen Hardt

We introduce a numerical solver for the spatially inhomogeneous Boltzmann equation using the Burnett spectral method. The modelling and discretization of the collision operator are based on the previous work [Z. Cai, Y. Fan, and Y. Wang,…

Computational Physics · Physics 2019-10-22 Zhicheng Hu , Zhenning Cai

We consider in this paper random batch interacting particle methods for solving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann (PB) equation as the equilibrium, in the external unbounded domain. To justify the…

Numerical Analysis · Mathematics 2022-03-25 Lei Li , Jian-Guo Liu , Yijia Tang

We study the iterative methods for large moment systems derived from the linearized Boltzmann equation. By Fourier analysis, it is shown that the direct application of the block symmetric Gauss-Seidel (BSGS) method has slower convergence…

Numerical Analysis · Mathematics 2024-07-11 Xiaoyu Dong , Zhenning Cai

A simplified relativistic kinetic theory for gases with internal degrees of freedom, based on a BGK-type collision term, is considered. First the Boltzmann equation is rewritten in tetrad form and then thermal coefficients are determined to…

General Relativity and Quantum Cosmology · Physics 2026-04-13 Philip Semrén , Michael Bradley , João M. S. Oliveira , M. Piedade Machado Ramos

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

We propose a systematic methodology to derive the regularized thirteen-moment equations in the rarefied gas dynamics for a general class of linearized collision models. Detailed expressions of the moment equations are written down for all…

Fluid Dynamics · Physics 2020-05-13 Zhenning Cai , Yanli Wang

A numerically stable method to solve the discretized Boltzmann-Enskog equation describing the behavior of non ideal fluids under inhomogeneous conditions is presented. The algorithm employed uses a Lagrangian finite-difference scheme for…

Mesoscale and Nanoscale Physics · Physics 2015-06-04 Simone Melchionna , Umberto Marini Bettolo Marconi

We present a further theoretical extension to the kinetic theory based formulation of the lattice Boltzmann method of Shan et al (2006). In addition to the higher order projection of the equilibrium distribution function and a sufficiently…

Computational Physics · Physics 2009-11-11 Raoyang Zhang , Xiaowen Shan , Hudong Chen

We consider the existence of steady rarefied flows of polyatomic gas between two parallel condensed phases, where evaporation and condensation processes occur. To this end, we study the existence problem of stationary solutions in a…

Analysis of PDEs · Mathematics 2025-03-18 Ki-Nam Hong , Marwa Shahine , Seok-Bae Yun

The stochastic particle method based on Bhatnagar-Gross-Krook (BGK) or ellipsoidal statistical BGK (ESBGK) model approximates the pairwise collisions in the Boltzmann equation using a relaxation process. Therefore, it is more efficient to…

Computational Physics · Physics 2018-08-14 Fei Fei , Jun Zhang , Jing Li , ZhaoHui Liu

A class of high order asymptotic preserving (AP) schemes has been developed for the BGK equation in Xiong et. al. (2015) [37], which is based on the micro-macro formulation of the equation. The nodal discontinuous Galerkin (NDG) method with…

Numerical Analysis · Mathematics 2016-02-09 Tao Xiong , Jingmei Qiu