Fully dissipative relativistic lattice Boltzmann method in two dimensions

Coelho, Rodrigo C. V.; Mendoza, M.; Doria, Mauro M.; Herrmann, Hans J.

doi:10.1016/j.compfluid.2018.04.023

Cited by 20 publications

(17 citation statements)

References 60 publications

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“…Higher orders would most probably require different strategies, e.g. off-lattice schemes, which drastically improve the spatial resolution of the grid, but have as drawbacks the need for interpolation and the introduction of artificial dissipation effects [43,47,77]; we do not consider these strategies in this paper.…”

Section: Gauss-type Quadratures With Prescribed Abscissasmentioning

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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Section: Gauss-type Quadratures With Prescribed Abscissasmentioning

confidence: 99%

Relativistic lattice Boltzmann methods: Theory and applications

et al. 2020

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“…Further evidence is given when taking into consideration thermal conductivity. We consider a second benchmark, in which following [66], two parallel plates are kept at constant temperatures, T 0 and T 1 , T 1 − T 0 = ∆T . For sufficiently small values of ∆T , and consequently low velocities compared to the speed of light, Eq.…”

Section: Numerical Validationmentioning

confidence: 99%

Relativistic dissipation obeys Chapman-Enskog asymptotics: Analytical and numerical evidence as a basis for accurate kinetic simulations

et al. 2019

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We present an analytical derivation of the transport coefficients of a relativistic gas in (2 + 1) dimensions for both Chapman-Enskog (CE) asymptotics and Grad's expansion methods. We further develop a systematic calibration method, connecting the relaxation time of relativistic kinetic theory to the transport parameters of the associated dissipative hydrodynamic equations. Comparison of our analytical results and numerical simulations shows that the CE method correctly captures dissipative effects, while Grad's method does not, in agreement with previous analyses performed in the (3 + 1) dimensional case. These results provide a solid basis for accurately calibrated computational studies of relativistic dissipative flows.

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“…The present semiclassical LBM opens the way for the modeling of many other fluids such as made by bosons close to the Bose-Einstein condensation, as in Ref. [40]. The semiclassical LBM allows for the investigation of the hydrodynamic limit of the electronic flow of many 2D novel materials, such as graphene [15], topological insulators [12], Weyl systems [13] and the 2D metal Palladium cobaltate [14].…”

Section: Discussionmentioning

confidence: 87%

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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Fully dissipative relativistic lattice Boltzmann method in two dimensions

Cited by 20 publications

References 60 publications

Relativistic lattice Boltzmann methods: Theory and applications

Relativistic lattice Boltzmann methods: Theory and applications

Relativistic dissipation obeys Chapman-Enskog asymptotics: Analytical and numerical evidence as a basis for accurate kinetic simulations

Lattice Boltzmann method for semiclassical fluids

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