Application of moment equations to the mathematical simulation of gas microflows

Иванов, И. Э.; Kryukov, I. A.; Timokhin, M. Yu.

doi:10.1134/s0965542513100084

Cited by 15 publications

(10 citation statements)

References 29 publications

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“…Additionally, suitable numerical methods to solve moment equations are still being developed. Finite volume approaches have been presented by Brown (1999), Torrilhon (2006), and Cai & Li (2010), and finite differences have been used by Gu & Emerson (2007) and Ivanov et al (2013).…”

Section: Further Systems Of Moment Equationsmentioning

confidence: 99%

Modeling Nonequilibrium Gas Flow Based on Moment Equations

Torrilhon

2016

Annu. Rev. Fluid Mech.

184

158

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This article discusses the development of continuum models to describe processes in gases in which the particle collisions cannot maintain thermal equilibrium. Such a situation typically is present in rarefied or diluted gases, for flows in microscopic settings, or in general whenever the Knudsen number-the ratio between the mean free path of the particles and a macroscopic length scale-becomes significant. The continuum models are based on the stochastic description of the gas by Boltzmann's equation in kinetic gas theory. With moment approximations, extended fluid dynamic equations can be derived, such as the regularized 13-moment equations. Moment equations are introduced in detail, and typical results are reviewed for channel flow, cavity flow, and flow past a sphere in the low-Mach number setting for which both evolution equations and boundary conditions are well established. Conversely, nonlinear, high-speed processes require special closures that are still under development. Current approaches are examined, along with the challenge of computing shock wave profiles based on continuum equations. 429

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Section: Further Systems Of Moment Equationsmentioning

confidence: 99%

Modeling Nonequilibrium Gas Flow Based on Moment Equations

Torrilhon

2016

Annu. Rev. Fluid Mech.

184

158

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“…The variant of high resolution Godunov scheme with linear flow parameter reconstruction is chosen for numerical solution of the R13 set of equations [21]. The second-order accuracy in space for smooth solutions is achieved using essentially two-dimensional reconstruction procedures [12,21] for the primitive variables within each computational cell. The standard central difference approximation is used for elliptical part discretization of the fluxes (diffusion terms).…”

Section: Methodsmentioning

confidence: 99%

“…The difference between them lies in the relations for higher order moments [8,9]. It has been shown that all variants are well applicable for numerical modelling of the moderately rarefied slow gas flows and allow the modelling of main nonequilibrium effects in low-velocity micro-flow problems [10,11,12,13,14,15,16,17] and some moderately rarefacted supersonic flows [5,18,19,15,20,21,22]. The difficulty is that the solid wall boundary conditions for R13 equations were obtained from one of the variants [10] which is not applicable to near hypersonic flows [9].…”

Section: Introductionmentioning

confidence: 99%

R13 moment equations applied to supersonic flow with solid wall interaction

Timokhin¹,

Struchtrup²,

Kokhanchik³

et al. 2019

31st International Symposium on Rarefied Gas Dynamics: Rgd31

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R13 moment set of equations is the regularization of original Grad 13-moment system. Several variants of R13 equations were presented after the first publication. The difference between them lies in the relations for higher order moments. It has been shown that all variants are well applicable for numerical modelling of the moderately rarefied slow gas flows and allow the modelling of main nonequilibrium effects in micro-flow problems. The difficulty is that the solid wall boundary conditions for R13 equations were obtained from one of the variants which is not applicable to near hypersonic flows. This study is devoted to the demonstration of the numerical results of R13 linear and nonlinear variants for supersonic flow over the flat plate. The R13 numerical solutions are compared with DSMC results computed by the SMILE++ software system.

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“…It is studied using direct simulation Monte‐Carlo (DSMC) to analyze the effect of incomplete surface accommodation on heat transfer and low speed rarefied flows, in a whole range of the Knudsen number compared with BGK model . The lid‐driven cavity is treated with the regularized 13‐moment method (R13) compared with DSMC and other macroscopic methods, showing then the accuracy of the R13 method in the description of the flow features in the transition regime . Similar works are done for the high nonequilibrium gas flow within a cavity using the DSMC method.…”

Section: Introductionmentioning

confidence: 99%

Rarefaction and external force effects on gas microflow in a lid‐driven cavity

Baliti

Hssikou

Alaoui

2018

Heat Trans. Asian Res.

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In this paper, the regularized 13‐moment approach (R13) is used to investigate the rarefaction effect on rarefied gas flow within a lid‐driven cavity. We will discuss the validity domain of the Navier‐Stokes and Fourier (NSF) solutions using the first order of velocity slip and temperature jump boundary conditions (NSF) and the regularized 10‐moments (R10) in slip and early transition regime. The effect of an external body force is examined in different directions according to the cavity inclination angle. A Maxwell monatomic gas is considered to study the flow and thermal characteristics within the lid‐driven cavity. The NSF method correctly describes the velocity profiles, but it captures only the trend of other macroscopic parameters. The NSF heat flux, which is found to be from the hot regions to the cold ones, loses its validity in the slip regime and beyond to predict an inverted heat flux predicted by both regularized models. Contrary to the R10, which can capture the rarefaction effect in the whole slip regime. The dimensionless shear stress tends to grow by increasing the rarefaction along the moving wall. The external body force affects the shear stress and velocity streamlines symmetry and creates an additional vortex, depending on the inclination angle.

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Application of moment equations to the mathematical simulation of gas microflows

Cited by 15 publications

References 29 publications

Modeling Nonequilibrium Gas Flow Based on Moment Equations

Modeling Nonequilibrium Gas Flow Based on Moment Equations

R13 moment equations applied to supersonic flow with solid wall interaction

Rarefaction and external force effects on gas microflow in a lid‐driven cavity

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