Rayleigh-Bénard instability in graphene

Furtmaier, O.; Mendoza, M.; Karlin, Iliya V.; Succi, Sauro; Herrmann, Hans J.

doi:10.1103/physrevb.91.085401

Cited by 15 publications

(25 citation statements)

References 34 publications

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“…However, in Ref. [40], the shear viscosity and the thermal conductivity, numerically measured using a RLBM for graphene, disagree with the ones obtained with Grad's expansion. Furthermore, the bulk viscosity was also calculated in Ref.…”

Section: Introductionmentioning

confidence: 81%

“…Recently, a new RLBM, also based on a third order expansion of the MJ distribution, was able to implement exact streaming on a square lattice without loosing spatial resolution allowing also to treat the regime of massive particles [38]. Meanwhile, other RLBMs with exact streaming have been used for graphene, where the grid points are disposed on a hexagonal lattice [39,40] such as in the molecular structure of graphene. Nevertheless, for these quadratures, the polynomial expansion of the EDF is limited to second order, which might be enough for practical purposes, but gives a poor description if the velocities and/or the temperature fluctuations are moderately high, as shown here.…”

Section: Introductionmentioning

confidence: 99%

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Fully dissipative relativistic lattice Boltzmann method in two dimensions

et al. 2018

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In this paper, we develop and characterize the fully dissipative Lattice Boltzmann method for ultra-relativistic fluids in two dimensions using three equilibrium distribution functions: Maxwell-Jüttner, Fermi-Dirac and Bose-Einstein. Our results stem from the expansion of these distribution functions up to fifth order in relativistic polynomials. We also obtain new Gaussian quadratures for square lattices that preserve the spatial resolution. Our models are validated with the Riemann problem and the limitations of lower order expansions to calculate higher order moments are shown. The kinematic viscosity and the thermal conductivity are numerically obtained using the Taylor-Green vortex and the Fourier flow respectively and these transport coefficients are compared with the theoretical prediction from Grad's theory. In order to compare different expansion orders, we analyze the temperature and heat flux fields on the time evolution of a hot spot.

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Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Fully dissipative relativistic lattice Boltzmann method in two dimensions

et al. 2018

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“…Finally, several authors have attempted to adapt RLBM schemes to the study of (2 + 1)dimensional relativistic hydrodynamics, motivated by the interest for the study of pseudo-relativistic systems such as the electrons flow in graphene. A series of theoretical works have taken into consideration the possibility of observing Rayleigh-Bénard instability [49,50], Kelvin-Helmholtz instability [51], current whirlpools [52], as well as preturbulent regimes [53,54] in a electronic fluid.…”

Section: Introductionmentioning

confidence: 99%

Relativistic lattice Boltzmann methods: Theory and applications

et al. 2020

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We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design relativistic LB schemes capable of bridging the gap between the ultra-relativistic regime, k B T mc 2 , and the non-relativistic one, k B T mc 2 . We further develop a systematic derivation of the transport coefficients as a function of the kinetic relaxation time in d = 1, 2, 3 spatial dimensions. The latter step allows to establish a quantitative bridge between the parameters of the kinetic model and the macroscopic transport coefficients. This leads to accurate calibrations of simulation parameters and is also relevant at the theoretical level, as it provides neat numerical evidence of the correctness of the Chapman-Enskog procedure. We present an extended set of validation tests, in which simulation results based on the RLBMs are compared with existing analytic or semi-analytic results in the mildly-relativistic (k B T ∼ mc 2 ) regime for the case of shock propagations in quark-gluon plasmas and laminar electronic flows in ultra-clean graphene samples. It is hoped and expected that the material collected in this paper may allow the interested readers to reproduce the present results and generate new applications of the RLBM scheme.

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“…One of the clear signals of its hydrodynamical regime is the onset of whirlpools (vortices) that has been predicted and subsequently observed [18,19,20,15]. The Dirac fluid of electron has been simulated by a relativistic LBM many times [21,22,23,24,25,26] in order to unveil new properties of graphene. These authors expand the FD distribution in orthogonal polynomials, similarly as done here, but using a fully relativistic formalism for massless particles (see Ref.…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann method for semiclassical fluids

Coelho

Doria

2018

Computers & Fluids

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We determine properties of the lattice Boltzmann method for semiclassical fluids, which is based on the Boltzmann equation and the equilibrium distribution function is given either by the Bose-Einstein or the Fermi-Dirac ones. New D-dimensional polynomials, that generalize the Hermite ones, are introduced and we find that the weight that renders the polynomials orthonormal has to be approximately equal, or equal, to the equilibrium distribution function itself for an efficient numerical implementation of the lattice Boltzmann method. In light of the new polynomials we discuss the convergence of the series expansion of the equilibrium distribution function and the obtainment of the hydrodynamic equations. A discrete quadrature is proposed and some discrete lattices in one, two and three dimensions associated to weight functions other than the Hermite weight are obtained. We derive the forcing term for the LBM, given by the Lorentz force, which dependents on the microscopic velocity, since the bosonic and fermionic particles can be charged. Motivated by the recent experimental observations of the hydrodynamic regime of electrons in graphene, we build an isothermal lattice Boltzmann method for electrons in metals in two and three dimensions. This model is validated by means of the Riemann problem and of the Poiseuille flow. As expected for electron in metals, the Ohm's law is recovered for a system analogous to a porous medium.

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Rayleigh-Bénard instability in graphene

Cited by 15 publications

References 34 publications

Fully dissipative relativistic lattice Boltzmann method in two dimensions

Fully dissipative relativistic lattice Boltzmann method in two dimensions

Relativistic lattice Boltzmann methods: Theory and applications

Lattice Boltzmann method for semiclassical fluids

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