Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion

Coelho, Rodrigo C. V.; Ilha, Anderson; Doria, Mauro M.; Pereira, R. M.; Aibe, V Y

doi:10.1103/physreve.89.043302

Cited by 13 publications

(34 citation statements)

References 30 publications

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“…Thermal fluctuations are taken into account by adding a random noise to those relaxed moments of the multiple relaxation time scheme which correspond to elements of the stress tensor [58,62]. We note that our approach using thermal fluctuations is different from considering a separate temperature field [63][64][65] as e.g. required for convection flows [63].…”

Section: 1 Lattice-boltzmann Methods For Fluid Dynamicsmentioning

confidence: 99%

Computational modeling of active deformable membranes embedded in three-dimensional flows

Bächer

Gekle

2019

Phys. Rev. E

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Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational algorithm to compute the dynamic evolution of an arbitrarily shaped, deformable thin membrane of active material embedded in a 3D flowing liquid. For this, our algorithm combines active gel theory with the classical theory of thin elastic shells. To compute the actual forces resulting from active stresses, we apply a parabolic fitting procedure to the triangulated membrane surface. Active forces are then dynamically coupled via an Immersed-Boundary method to the surrounding fluid whose dynamics can be solved by any standard, e.g. Lattice-Boltzmann, flow solver. We validate our algorithm using the Green's functions of [Berthoumieux et al. New J. Phys. 16, 065005 (2014)] for an active cylindrical membrane subjected (i) to a locally increased active stress and (ii) to a homogeneous active stress. For the latter scenario, we predict in addition a so far unobserved non-axisymmetric instability. We highlight the versatility of our method by analyzing the flow field inside an actively deforming cell embedded in external shear flow. Further applications may be cytoplasmic streaming or active membranes in blood flows. Published as: Phys. Rev. E 99(6), 062418 (2019)

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Section: 1 Lattice-boltzmann Methods For Fluid Dynamicsmentioning

confidence: 99%

Computational modeling of active deformable membranes embedded in three-dimensional flows

Bächer

Gekle

2019

Phys. Rev. E

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“…Here, the normalization factor is the same as for the Hermite polynomials in D-dimensions [24,54], where we define δ i 1 ···i N | j 1 ··· j N ≡ δ i 1 j 1 · · · δ i N j N + all permutations of j's and δ i j is the Kronecker's delta. The weight functions used to build the models in this paper will be discussed in the next section (Eqs.…”

Section: Relativistic Polynomialsmentioning

confidence: 99%

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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“…Here the normalization factor is the same as for the Hermite polynomials in D-dimensions [41,62], where we define δ i1···iN |j1···jN ≡ δ i1j1 · · · δ iN jN + all permutations of j's and δ ij is the Kronecker's delta. Note that we have some polynomials with only spatial components (latin indexes) and others which include one temporal component (zero).…”

Section: B Expansion Of the Equilibrium Distribution Functionmentioning

confidence: 99%

“…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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Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion

Cited by 13 publications

References 30 publications

Computational modeling of active deformable membranes embedded in three-dimensional flows

Computational modeling of active deformable membranes embedded in three-dimensional flows

Fully dissipative relativistic lattice Boltzmann method in two dimensions

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

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