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Related papers: A Complete Set of Grad's Thirteen Regularized Mome…

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We present a number of exact solutions to the linearised Grad equations for non-equilibrium rarefied gas flows and heat flows. The solutions include the flow and pressure fields associated to a point force placed in a rarefied gas flow…

Fluid Dynamics · Physics 2022-12-02 Hollis Williams

The Boltzmann collision operator for a dilute granular gas of inelastic rough hard spheres is much more intricate than its counterpart for inelastic smooth spheres. Now the one-body distribution function depends not only on the…

Soft Condensed Matter · Physics 2014-11-10 Andrés Santos

Recently, Pennisi and Ruggeri [J Stat Phys 179, 231-246 (2020)] consider the classical limit of the relativistic theory of moments associated with the Boltzmann-Chernikov equation truncated at a tensorial index $N+1$ and they proved that…

Statistical Mechanics · Physics 2021-01-01 Takashi Arima , Tommaso Ruggeri

Based on a Boltzmann-like traffic equation for aggressive drivers we construct in this paper a second-order continuum traffic model which is similar to the Navier-Stokes equations for viscous fluids by applying two well-known methods of…

Mathematical Physics · Physics 2010-12-01 W. Marques , A. R. Mendez

A thermohydrodynamic lattice-BGK model for the ideal gas was derived by Alexander et al. in 1993, and generalized by McNamara et al. in the same year. In these works, particular forms for the equilibrium distribution function and the…

comp-gas · Physics 2015-06-24 Bruce M. Boghosian , Peter V. Coveney

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

The existing kinetic theory of gases is based on an analytical approach that becomes intractable for all but the simplest molecules. Here we propose a simple numerical scheme to compute the transport properties of molecular gases in the…

Soft Condensed Matter · Physics 2020-08-25 Xipeng Wang , Simón Ramírez-Hinestrosa , Daan Frenkel

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

In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not…

Nuclear Theory · Physics 2015-06-04 G. S. Denicol , H. Niemi , E. Molnar , D. H. Rischke

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of the distribution functions. The collisional moments are shown to be…

Plasma Physics · Physics 2017-05-24 David Pfefferlé , Eero Hirvijoki , Manasvi Lingam

Most numerical schemes proposed for solving BGK models for rarefied gas dynamics are based on the discrete velocity approximation. Since such approach uses fixed velocity grids, one must secure a sufficiently large domain with fine velocity…

Numerical Analysis · Mathematics 2022-04-20 Sebastiano Boscarino , Seung Yeon Cho , Giovanni Russo

The transport coefficients for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($\alpha$) and tangential ($\beta$) restitution are obtained in a unified framework as functions of the…

Soft Condensed Matter · Physics 2021-09-14 Alberto Megías , Andrés Santos

We point out that the quantum Grad's 13-moment system [R. Yano, Physica A: Statistical Mechanics and its Applications, 416:231-241, 2014] is lack of global hyperbolicity, and even worse, the thermodynamic equilibrium is not an interior…

Mathematical Physics · Physics 2017-04-26 Yana Di , Yuwei Fan , Ruo Li

Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially non-trivial velocity distributions. In this paper, moment equations for the bulk velocities,…

Mathematical Physics · Physics 2023-10-20 Evan Habbershaw , Ryan S. Glasby , Jeffrey R. Haack , Cory D. Hauck , Steven M. Wise

The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation allows for efficient flow simulations, especially in the transition regime between continuum and high rarefaction. However, ensuring efficient performances for multiscale…

Fluid Dynamics · Physics 2025-05-09 Félix Garmirian , Marcel Pfeiffer

The Borgnakke-Larsen model, widely used in rarefied flow predictions, serves as the mainstream energy-exchange kernel for polyatomic gases. However, it lacks integrability and does not guarantee detailed balance, limiting theoretical…

Computational Physics · Physics 2026-04-02 Sha Liu , Ningchao Ding , Ming Fang , Hao Jin , Rui Zhang , Congshan Zhuo , Chengwen Zhong

In this paper, we present a regularization to 1D Grad's moment system to achieve global hyperbolicity. The regularization is based on the observation that the characteristic polynomial of the Jacobian of the flux in Grad's moment system is…

Mathematical Physics · Physics 2012-07-04 Zhenning Cai , Yuwei Fan , Ruo Li

A Maxwell gas confined within a micro cavity with non-isothermal walls is investigated in the slip and early transition regimes using the classical and extended continuum theories. The vertical sides of the cavity are kept at the uniform…

Fluid Dynamics · Physics 2019-04-18 Mohamed Hssikou , Jamal Baliti , Mohammed Alaoui

A description of Orthogonal Tensor Hermite Polynomials in 3-D is presented. These polynomials, as introduced by Grad in 1949 [1], can be used to obtain a series solution to the Boltzmann Transport Equation. The properties that are explored…

Mathematical Physics · Physics 2014-12-01 Parul Maheshwari , Gautam Mukhopadhyay , Siddhartha SenGupta