Origin of density clustering in a freely evolving granular gas

Brey, J. Javier; Ruiz‐Montero, M. J.; Cubero, David

doi:10.1103/physreve.60.3150

Cited by 99 publications

(98 citation statements)

References 12 publications

(1 reference statement)

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“…Unstable vorticity modes initially grow as predicted by the linear stability analysis, but eventually saturate because of nonlinear viscous heating. The influence of nonlinear viscous heating on the formation of temperature inhomogeneities and clustering has been pointed out by Goldhirsch and Zanetti [9], and investigated in more detail by Brey et al [31], by comparing the results of a hydrodynamic model with viscous heating, using direct Monte Carlo simulation of the Boltzmann equation.…”

Section: Discussionmentioning

confidence: 99%

“…We finally remark that several authors have also studied nonlinear terms in the macroscopic equations for granular fluids, such as the viscous heating term [9,31,12,32], and the nonlinear convective term [11]. The inclusion of the combined effects of viscous heating and collisional cooling is essentially the new mechanism driving the dynamics of dissipative granular fluids in the time regime, directly following the homogeneous cooling state.…”

Section: Dynamic Equations and Instabilitiesmentioning

confidence: 99%

“…[9] in MD simulations of a fluid of two-dimensional hard disks, and in Ref. [31] in Direct Monte Carlo simulations of the Boltzmann equation for an IHS gas. Figure 7 shows the observed density and temperature inhomogeneities.…”

Section: Md-simulationsmentioning

confidence: 99%

“…The search for the proper macroscopic description of unstable granular fluids has been pursued by many authors [1][2][3][4][5][6][7][8][9][10][11][12][13]18,20,[22][23][24][25][26][27][28][29][30][31][32]. Recently, two new points of view have been presented, namely by Ben-Naim et al [11] and by Soto et al [12].…”

Section: Introductionmentioning

confidence: 99%

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Wakou

Brito

Ernst

2002

Journal of Statistical Physics

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In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau-Ginzburg (LG) models for critical and unstable fluids (e.g. spinodal decomposition). The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field.Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.

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Section: Discussionmentioning

confidence: 99%

Section: Dynamic Equations and Instabilitiesmentioning

confidence: 99%

Section: Md-simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Wakou

Brito

Ernst

2002

Journal of Statistical Physics

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“…Assuming the strong inequalities (1), one can use the following set of hydrodynamic equations [32,33,38]. The continuity equation,…”

Section: A Governing Equations and Boundary Conditionsmentioning

confidence: 99%

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

2010

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We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrowsector-shaped container. Here the HCS loses its stability via a transcritical bifurcation. For some initial conditions a time-independent inhomogeneous density profile sets in, qualitatively similar to that previously found in a narrow-channel geometry. For other initial conditions, however, the dilute gas develops thermal collapse unarrested by heat diffusion. We determine the dynamic scalings of the flow close to collapse analytically and verify them in hydrodynamic simulations. The results of this work imply that, in dimension higher than one, Navier-Stokes hydrodynamics of a dilute granular gas is prone to finite-time density blowups. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.

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Cluster Instability in Freely Evolving Granular Gases

Brey

2001

Coherent Structures in Complex Systems

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Origin of density clustering in a freely evolving granular gas

Cited by 99 publications

References 12 publications

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Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

Cluster Instability in Freely Evolving Granular Gases

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