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

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Efficient modeling of rarefied flow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad's distribution function for 13 moments-based moment gas kinetic solver (G13-MGKS) and the…

Fluid Dynamics · Physics 2022-07-20 W. Liu , Z. J. Liu , Z. L. Zhang , C. J. Teo , C. Shu

It is essential to efficiently solve multiscale flows covering the continuum regime to the rarefied regime. The explicit form of Grad's 13 moments distribution function-based moment gas kinetic solver (G13-MGKS) has been proposed in our…

Fluid Dynamics · Physics 2024-03-26 W. Liu , C. Shu , Z. J. Liu

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

We introduce a numerical method for solving Grad's moment equations or regularized moment equations for arbitrary order of moments. In our algorithm, we do not need explicitly the moment equations. As an instead, we directly start from the…

Mathematical Physics · Physics 2010-05-04 Zhenning Cai , Ruo Li

In (Commun Pure Appl Math 2(4):331-407, 1949), Grad proposed a Hermite series expansion for approximating solutions to kinetic equations that have an unbounded velocity space. However, for initial boundary value problems, poorly imposed…

Numerical Analysis · Mathematics 2023-03-01 Neeraj Sarna , Jan Giesselmann , Manuel Torrilhon

Mixtures of relativistic gases are analyzed within the framework of Boltzmann equation by using Grad's moment method. A relativistic mixture of $r$ constituent is characterized by the moments of the distribution function: particle…

Statistical Mechanics · Physics 2013-09-16 Gilberto M. Kremer , Wilson Marques

We develop the steady-state regularized 13-moment equations in the linear regime for rarefied gas dynamics with general collision models. For small Knudsen numbers, the model is accurate up to the super-Burnett order, and the resulting…

Fluid Dynamics · Physics 2023-03-14 Zhenning Cai , Manuel Torrilhon , Siyao Yang

We use guiding principles from nonequilibrium thermodynamics to develop an admissible set of 13 moment equations for rarefied gas flows. The main benefits of our thermodynamic approach are an explicit entropy expression fulfilling an $H$…

Statistical Mechanics · Physics 2010-11-10 Hans Christian Öttinger

We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas,…

Astrophysics · Physics 2009-11-06 Xinzhong Chen , Hongling Rao , Edward A. Spiegel

A kinetic theory for moderately dense gases of inelastic and rough spherical molecules is developed from the Enskog equation where a macroscopic state is characterized by 29 scalar fields which correspond to the moments of the distribution…

Statistical Mechanics · Physics 2024-08-02 Gilberto M. Kremer

The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done…

Fluid Dynamics · Physics 2009-11-10 Edward A. Spiegel , Jean-Luc Thiffeault

Grad's method of moments is employed to develop higher-order Grad's moment equations---up to first 26-moments---for granular gases within the framework of the (inelastic) Boltzmann equation. The homogeneous cooling state of a freely cooling…

Soft Condensed Matter · Physics 2019-09-16 Vinay Kumar Gupta , Priyanka Shukla , Manuel Torrilhon

The Navier-Stokes transport coefficients for a granular gas of smooth inelastic hard disks or spheres are determined from the inelastic Boltzmann equation by means of Grad's moment method. The shear viscosity $\eta$, the thermal…

Statistical Mechanics · Physics 2015-06-12 V. Garzó

In this paper, we propose a globally hyperbolic regularization to the general Grad's moment system in multi-dimensional spaces. Systems with moments up to an arbitrary order are studied. The characteristic speeds of the regularized moment…

Mathematical Physics · Physics 2012-03-05 Zhenning Cai , Yuwei Fan , Ruo Li

The Navier-Stokes transport coefficients of a granular dense fluid of smooth inelastic hard disks or spheres are explicitly determined by solving the inelastic Enskog equation by means of Grad's moment method. The transport coefficients are…

Statistical Mechanics · Physics 2013-06-27 Vicente Garzó

The Navier-Stokes transport coefficients for a model of a confined quasi-two-dimensional granular gas of smooth inelastic hard spheres are derived from the Enskog kinetic equation. A normal solution to this kinetic equation is obtained via…

Statistical Mechanics · Physics 2026-02-26 Vicente Garzó , Ricardo Brito , Rodrigo Soto

The goal of this note is to provide most of the technical details involved in the application of the Chapman-Enskog method to solve the revised Enskog equation to Navier-Stokes order. Explicit expressions for the transport coefficients and…

Statistical Mechanics · Physics 2012-11-14 Vicente Garzó

The classical problem of steady rarefied gas flow past an infinitely thin circular disk is revisited, with particular emphasis on the gas behavior near the disk edge. The uniform flow is assumed to be perpendicular to the disk surface. An…

Fluid Dynamics · Physics 2026-01-26 Takuma Tomita , Satoshi Taguchi , Tetsuro Tsuji

The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the…

Statistical Mechanics · Physics 2014-09-03 Gilberto M. Kremer , Andrés Santos , Vicente Garzó

Modelling rarefied gas flow via the Boltzmann equation plays a vital role in many areas. Due to the high dimensionality of this kinetic equation and the coexistence of multiple characteristic scales in the transport processes, conventional…

Numerical Analysis · Mathematics 2025-05-27 Wei Su , Xi Zou
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