Special issues on moment methods in kinetic gas theory

Torrilhon, Manuel

doi:10.1007/s00161-009-0129-x

Cited by 22 publications

(18 citation statements)

References 25 publications

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“…10 An overview of the equations and their features can be found in Ref. 11, the special issues, 12 and in the text book. 13 The R13 equations deliver quantitatively correct results for Knudsen numbers up to 0.5 or, in some processes, up to KnϷ 1.…”

Section: Introductionmentioning

confidence: 99%

Slow gas microflow past a sphere: Analytical solution based on moment equations

Torrilhon

2010

Physics of Fluids

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The regularized 13-moment equations are solved analytically for the microflow of a gas past a sphere in the case of low Mach numbers. The result is given in fully explicit expressions and shows nontrivial behavior for all fluid fields including stress, heat flux, and temperature. Various aspects of the flow such as temperature polarization and total force are reproduced correctly for moderate Knudsen number. The analytical solution allows studying the rise of Knudsen layers and their interaction and coupling to the fluid variables in the bulk. Additionally, based on the regularized 13-moment equations system, hybrid boundary conditions are given for the standard Stokes equations in order to enable them to predict nonequilibrium effects in the flow past a sphere.

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Section: Introductionmentioning

confidence: 99%

Slow gas microflow past a sphere: Analytical solution based on moment equations

Torrilhon

2010

Physics of Fluids

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“…A list of relevant publications can be found in the references of [13]. A list of relevant publications can be found in the references of [13].…”

Section: Introductionmentioning

confidence: 99%

“…During the past 20 years, as the investigation into the moment method has gone deeper, various "regularizations" have been proposed to challenge the traditional biases against the moment method. A list of relevant publications can be found in the references of [13]. Recently we became interested in the large moment system together with its numerical methods [2,3,4,5], and it was found that the lack of the well-posedness due to the loss of global hyperbolicity is a major obstacle in our simulations, especially for large Mach number gas flows [5].…”

Section: Introductionmentioning

confidence: 99%

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Globally Hyperbolic Regularization of Grad's Moment System

Cai

Fan

2013

Comm Pure Appl Math

118

162

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In this paper, we propose a globally hyperbolic regularization to the general Grad's moment system in multidimensional spaces. Systems with moments up to an arbitrary order are studied. The characteristic speeds of the regularized moment system can be analytically given and depend only on the macroscopic velocity and the temperature. The structure of the eigenvalues and eigenvectors of the coefficient matrix is fully clarified. The regularization together with the properties of the resulting moment systems is consistent with the simple onedimensional case discussed in [1]. In addition, all characteristic waves are proven to be genuinely nonlinear or linearly degenerate, and the studies on the properties of rarefaction waves, contact discontinuities, and shock waves are included. GLOBALLY HYPERBOLIC MOMENT SYSTEM 465 Ã C PROOF. Let i D N D .˛/, with j˛j Ä M . Then we need only to verify that (3.20) z A M .i; 1WN / r D r w i is always valid. Since A M is determined by (3.2), (3.3), and (3.4), and y A M and z A M are defined as in (3.11) and (3.13), respectively, we can write all entries of z A M . Now let us verify equation (3.20) case by case: (1) For˛D 0, z A M .1; N D .e 1 // D 1 is the only nonzero entry of z A M .1; 1WN /; hence, z A M .i; 1WN / r D 1 r u 1 D r D r w i :(2) For˛D e 1 , z A M .i; 1WN / r D 2 r p 2e 1 =2 D 2 r D r u 1 D r w i :(3) For˛D e k , k D 2; : : : ; D, z A M .i; 1WN / r D 1 r p e 1 Ce k =2 D r u k D r w i : ÃHe M 1 . / ZHENNING CAI

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“…Indeed the importance of the second-order hydrodynamics has been recognized and many attempts have been done to derive it [22,23,24,25,26,27], and among them the renormalization group (RG) method seems to be a promising method to derive the second-order hydrodynamics as well as the transport coefficients including the viscous relaxation times. In fact, it has been applied to derive the second-order hydrodynamic equations from the Boltzmann equation for both relativistic and non-relativistic systems [28,29,30,31], and desirable properties have been already proved for the resultant equation such as causality, stability, positivity of the entropy production rate, and the Onsager's recipro-cal relation without imposing any assumption a priori [31,32].…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic dynamics of fermionic cold atoms — Quantitative analysis of transport coefficients and relaxation times

2016

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We give a quantitative analysis of the dynamical properties of fermionic cold atomic gases in normal phase, such as the shear viscosity, heat conductivity, and viscous relaxation times, using the novel microscopic expressions derived by the renormalization group (RG) method, where the Boltzmann equation is faithfully solved to extract the hydrodynamics without recourse to any ansatz.In particular, we examine the quantum statistical effects, temperature dependence, and scattering-length dependence of the transport coefficients and the viscous relaxation times. The numerical calculation shows that the relation τ π = η/P , which is derived in the relaxation-time approximation (RTA) and is used in most of the literature, turns out to be satisfied quite well, while the similar relation for the viscous relaxation time τ J of the heat conductivity is satisfied only approximately with a considerable error.

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Special issues on moment methods in kinetic gas theory

Cited by 22 publications

References 25 publications

Slow gas microflow past a sphere: Analytical solution based on moment equations

Slow gas microflow past a sphere: Analytical solution based on moment equations

Globally Hyperbolic Regularization of Grad's Moment System

Mesoscopic dynamics of fermionic cold atoms — Quantitative analysis of transport coefficients and relaxation times

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