A lattice Boltzmann method based on generalized polynomials and its application for electrons in metals

Coelho, Rodrigo C. V.; Ilha, Anderson; Doria, Mauro M.

doi:10.1209/0295-5075/116/20001

Cited by 9 publications

(14 citation statements)

References 30 publications

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“…With this purpose, we calculate relativistic generalized polynomials following the procedure developed in Ref. [25] for non-relativistic polynomials. The polynomials below allow us to find orthogonal polynomials for generic weight functions, ω(p).…”

Section: Relativistic Polynomialsmentioning

confidence: 99%

“…The lattice Boltzmann method [21] (LBM) is a numerical technique based on the Boltzmann equation and on the Gaussian quadrature, which have been successfully applied to model classical fluids [22,23], governed by the Maxwell-Boltzmann (MB) distribution, and also to semi-classical [24,25,26] and relativistic fluids. For classical fluids, it has been demonstrated that the hydrodynamic equations can be fully recovered by the LBM if the equilibrium distribution function (EDF) is expanded in orthogonal polynomials up to a minimum order that retains the necessary moments [27,28].…”

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: Relativistic Polynomialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fully dissipative relativistic lattice Boltzmann method in two dimensions

et al. 2018

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“…The Lattice Boltzmann Method (LBM) [39,40] is a computational fluid dynamics technique based on the space-time discretization of the Boltzmann equation that has been successfully applied to simulate classical, semiclassical [41][42][43], quantum [44][45][46] and relativistic fluids. It has many advantages over other numerical methods as the facility to simulate flows through complex geometries and the easy implementation and parallelization of computational codes.…”

Section: Introductionmentioning

confidence: 99%

Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene

et al. 2017

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We provide numerical evidence that a Kelvin-Helmholtz instability occurs in the Dirac fluid of electrons in graphene and can be detected in current experiments. This instability appears for electrons in the viscous regime passing though a micrometer scale obstacle and affects measurements on the time scale of nanoseconds. A possible realization with a needle shaped obstacle is proposed to produce and detect this instability by measuring the electric potential difference between contact points located before and after the obstacle. We also show that, for our setup, the Kelvin-Helmholtz instability leads to the formation of whirlpools similar to the ones reported in Bandurin, D. A., et al. Science 351.6277 (2016): 1055-1058. To perform the simulations, we develop a new lattice Boltzmann method able to recover the full dissipation in a fluid of massless particles.

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“…However, other choices adapted to particular problems are possible. An example of this, are the generalized polynomials for electronic problems developed in [48].…”

Section: Lattice Wigner Schemementioning

confidence: 99%

Lattice Wigner equation

et al. 2018

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We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretisation, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one and two dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of threedimensional open systems is also illustrated.

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A lattice Boltzmann method based on generalized polynomials and its application for electrons in metals

Cited by 9 publications

References 30 publications

Fully dissipative relativistic lattice Boltzmann method in two dimensions

Fully dissipative relativistic lattice Boltzmann method in two dimensions

Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene

Lattice Wigner equation

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