Cross Correlators and Galilean Invariance in Fluctuating Ideal Gas Lattice Boltzmann Simulations

We analyze the Lattice Boltzmann method for the simulation of fluctuating hydrodynamics by Adhikari et al. [Europhys. Lett. 71, 473 (2005)] and find that it shows excellent agreement with theory even for small wavelengths as long as a stationary system is considered. This is in contrast to other finite difference and older lattice Boltzmann implementations that show convergence only in the limit of large wavelengths. In particular cross correlators vanish to less than 0.5%. For larger mean velocities, however, Galilean invariance violations manifest themselves through errors of a magnitude similar to those of the earlier implementations.Comment: 8 pages, 9 figures, DSFD 200

Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re) and Bingham number (Bn). These results reveal the flow behavior of Bingham plastics

Development of the PETAL Laser Facility and its Diagnostic Tools

The PETAL system (PETawatt Aquitaine Laser) is a high-energy short-pulse laser, currently in an advanced construction phase, to be combined with the French Mega-Joule Laser (LMJ). In a first operational phase (beginning in 2015 and 2016) PETAL will provide 1 kJ in 1 ps and will be coupled to the first four LMJ quads. The ultimate performance goal to reach 7PW (3.5 kJ with 0.5 ps pulses). Once in operation, LMJ and PETAL will form a unique facility in Europe for High Energy Density Physics (HEDP). PETAL is aiming at providing secondary sources of particles and radiation to diagnose the HED plasmas generated by the LMJ beams. It also will be used to create HED states by short-pulse heating of matter. Petal+ is an auxiliary project addressed to design and build diagnostics for experiments with PETAL. Within this project, three types of diagnostics are planned: a proton spectrometer, an electronspectrometer and a large-range X-ray spectrometer

Anomalous kinetics and transport from 1D self--consistent mode--coupling theory

We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant correlators are solved analytically and checked numerically. In particular, we find that the memory functions exhibit a power-law decay accompanied by relatively fast oscillations. Furthermore, the scaling behaviour and, correspondingly, the universality class depends on the order of the leading nonlinear term. In the cubic case, both viscosity and thermal conductivity diverge in the thermodynamic limit. In the quartic case, a faster decay of the memory functions leads to a finite viscosity, while thermal conductivity exhibits an even faster divergence. Finally, our analysis puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion

Wall Orientation and Shear Stress in the Lattice Boltzmann Model

The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near the staircase boundary. Finally, we calculate the wall shear stress in the human abdominal aorta in steady conditions using our method and compare the results with a standard finite volume solver and experimental data available in the literature. Applications of our ideas in a simplified protocol for data preprocessing in medical applications are discussed.Comment: 9 pages, 11 figure

Simulation of static critical phenomena in non-ideal fluids with the Lattice Boltzmann method

A fluctuating non-ideal fluid at its critical point is simulated with the Lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order-parameter.Comment: 23 pages, 16 figure

Lattice Boltzmann simulations of two-phase flow with high density ratio in axially symmetric geometry

In this paper, a two-phase lattice Boltzmann (LB) model, developed for simulating fluid flows on a Cartesian grid at high liquid-to-gas density ratios, is adapted to an axisymmetric coordinate system. This is achieved by incorporating additional source terms in the planar evolution equations for the density and pressure distribution functions such that the axisymmetric mass and momentum conservation equations are recovered in the macroscopic limit. Appropriate numerical treatment of the terms is performed to obtain stable computations at high density ratio for this axisymmetric model. The particle collision is modeled by employing multiple relaxation times to attain stability at low viscosity. The model is evaluated by verifying the Laplace-Young relation for a liquid drop, comparing computed frequency of oscillations of an initially ellipsoidal drop with analytical values and comparing the behavior of a spherical drop impinging on a wet wall with prior results. The time evolution of the radial distance of the tip of the corona, formed when the drop impinges, agrees well with prior data.Shiladitya Mukherjee and John Abraha

Fluidic gates simulated with lattice Boltzmann method under different Reynolds numbers

© 2018 Elsevier B.V. Fluidic devices use fluid as a medium for information transfer and computation. Boolean values are represented by the presence of fluid jets in the input and output channels. Velocity of a fluid is one of the parameters determining Reynolds number of the flow. Reynolds number is a parameter that characterizes the behaviour of the flow: laminar, transient or turbulent. Using lattice Boltzmann method we study the behaviour of fluidic gates for various Reynolds numbers. On the designs of AND and OR gates we show the fluidic gates remain functional even for low Reynolds numbers, like 100. The gates designed can be cascaded into functional logical circuits

Generation of α-Particle Beams With a Multi-kJ, Peta-Watt Class Laser System

We present preliminary results on generation of energetic α-particles driven by lasers. The experiment was performed at the Institute of Laser Engineering in Osaka using the short-pulse, high-intensity, high-energy, PW-class laser. The laser pulse was focused onto a thin plastic foil (pitcher) to generate a proton beam by the well-known TNSA mechanism which, in turn, was impinging onto a boron-nitride (BN) target (catcher) to generated alpha-particles as a result of proton-boron nuclear fusion events. Our results demonstrate generation of α-particles with energies in the range 8–10 MeV and with a flux around 5 × 10^9 sr^−1

Large Colloids in Cholesteric Liquid Crystals

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