Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients

Megías, Alberto; Santos, Andrés

doi:10.1103/physreve.104.034901

Cited by 8 publications

(14 citation statements)

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“…An immediate application of this work is the use of the closed set of NSF hydrodynamic equations to analyze the stability of the HCS, again in a unified framework encompassing the special HS and HD cases. This is the subject of the companion paper [48]. Additionally, the extension of the results to stochastically driven granular gases is straightforward (since the evaluation of the collision integrals has already been done in the present paper) and will be published elsewhere.…”

Section: Discussionmentioning

confidence: 87%

Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients

Megías,

Santos

2021

Preprint

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The transport coefficients for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal (α) and tangential (β) restitution are obtained in a unified framework as functions of the number of translational (dt) and rotational (dr) degrees of freedom. The derivation is carried out by means of the Chapman-Enskog method with a Sonine-like approximation in which, in contrast to previous approaches, the reference distribution function for angular velocities does not need to be specified. The well-known case of purely smooth d-dimensional particles is recovered by setting dt = d and formally taking the limit dr → 0. In addition, previous results [G. M. Kremer, A. Santos, and V. Garzó, Phys. Rev. E 90, 022205 (2014)] for hard spheres are reobtained by taking dt = dr = 3, while novel results for hard-disk gases are derived with the choice dt = 2, dr = 1. The singular quasismooth limit (β → −1) and the conservative Pidduck's gas (α = β = 1) are also obtained and discussed.

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Section: Discussionmentioning

confidence: 87%

Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients

Megías,

Santos

2021

Preprint

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“…In these equations, D t = ∂ t + u • ∇ is the material time derivative, τ t is the HCS translational-to total temperature ratio, ζ (0) is the Euler-order cooling rate, η is the shear viscosity, η b is the bulk viscosity, λ is the thermal conductivity, µ is a Dufour-like transport coefficient, and ξ is a dimensionless transport coefficient associated with the velocity-divergence contribution to the cooling rate [16]. Dimensional analysis dictates that…”

Section: Navier-stokes-fourier Hydrodynamic Equationsmentioning

confidence: 99%

“…In general, each particle is animated with d t components of the translational velocity v and d r components of the angular velocity ω, where (d t , d r ) = (3,3) and (2,1) for HS and HD, respectively. Our main aim is to perform a linear stability analysis of the homogeneous cooling state (HCS) of the granular gas by means of a Navier-Stokes-Fourier (NSF) hydrodynamic description in terms of the number of translational (d t ) and rotational (d r ) degrees of freedom, thus encompassing the HS and HD systems within a unified treatment, as done in previous works [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…To that end, we make explicit use of the approximate expressions for the NSF transport coefficients derived in the companion paper I [16]. The HS results [10] are re-covered by setting (d t , d r ) = (3,3), while novel results, to the best of our knowledge, are presented for HD by the choice (d t , d r ) = (2, 1).…”

Section: Introductionmentioning

confidence: 99%

“…IV, use is made of the approximate transport coefficients computed in Ref. [16] and the results of the stability analysis are discussed. To clarify some unexpected outcomes in the HD case, our MD simulation results are exposed in Sec.…”

Section: Introductionmentioning

confidence: 99%

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Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. II. Stability analysis

Megías,

Santos

2021

Preprint

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Conditions for the stability under linear perturbations around the homogeneous cooling state are studied for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal (α) and tangential (β) restitution. After a formally exact linear stability analysis of the Navier-Stokes-Fourier hydrodynamic equations in terms of the translational (dt) and rotational (dr) degrees of freedom, the transport coefficients derived in the companion paper [A. Megías and A. Santos, "Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients"] are employed. Known results for hard spheres [V. Garzó, A. Santos, and G. M. Kremer, Phys. Rev. E 97, 052901 (2018)] are recovered by setting dt = dr = 3, while novel results for hard disks (dt = 2, dr = 1) are obtained. In the latter case, a high-inelasticity peculiar region in the (α, β) parameter space is found, inside which the critical wave number associated with the longitudinal modes diverges. Comparison with event-driven molecular dynamics simulations for hard disks shows that this region of absolute instability may be an artifact of the extrapolation to high inelasticity of the approximations made in the derivation of the transport coefficients, although it signals a strong unstable characterization of this parameter zone. In the case of moderate inelasticity (α = 0.7), on the other hand, a good agreement between the theoretical predictions and the simulation results is found.

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Granular Gas of Inelastic and Rough Maxwell Particles

Kremer

Santos

2022

J Stat Phys

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The most widely used model for granular gases is perhaps the inelastic hard-sphere model (IHSM), where the grains are assumed to be perfectly smooth spheres colliding with a constant coefficient of normal restitution. A much more tractable model is the inelastic Maxwell model (IMM), in which the velocity-dependent collision rate is replaced by an effective mean-field constant. This simplification has been taken advantage of by many researchers to find a number of exact results within the IMM. On the other hand, both the IHSM and IMM neglect the impact of roughness—generally present in real grains—on the dynamic properties of a granular gas. This is remedied by the inelastic rough hard-sphere model (IRHSM), where, apart from the coefficient of normal restitution, a constant coefficient of tangential restitution is introduced. In parallel to the simplification carried out when going from the IHSM to the IMM, we propose in this paper an inelastic rough Maxwell model (IRMM) as a simplification of the IRHSM. The tractability of the proposed model is illustrated by the exact evaluation of the collisional moments of first and second degree, and the most relevant ones of third and fourth degree. The results are applied to the evaluation of the rotational-to-translational temperature ratio and the velocity cumulants in the homogeneous cooling state.

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Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients

Cited by 8 publications

References 55 publications

Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients

Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients

Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. II. Stability analysis

Granular Gas of Inelastic and Rough Maxwell Particles

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