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In this paper, we highlight the benefits resulting from imposing energyconserving equilibria in entropic lattice Boltzmann models for isothermal flows. The advantages are documented through a series of numerical simulations, such as TaylorGreen vortices, cavity flow and flow past a sphere.

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A generalanalysis of the hydrodynamic limit of multi-relaxationtime lattice Boltzmann models is presented. We examine multi-relaxation time BGK collision operators that are constructed similarly to those for the MRT case, however, without explicitly moving into a moment space representation. The corresponding ’moments’ are derived as left eigenvectors of said collision operator in velocity space. Consequently we can, in a representation independent of the chosen base velocity set, generate the conservation equations. We find a significant degree of freedom in the choice of the collision matrix and the associated basis which leaves the collision operator invariant. We explain why MRT implementations in the literature reproduce identical hydrodynamics despitebeing basedondifferentorthogonalizationrelations. Moreimportantly, however, we outline a minimal set of requirements on the moment base necessary to maintain the validity of the hydrodynamic equations. This is particularly useful in the context of position and time-dependent moments such as those used in the context of peculiar velocities and some implementations of fluctuations in a lattice-Boltzmann simulation. 

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AnalternateBGKtypeformulationoftheEnskog equationhasbeenrecently proposed [1]. It wasshown that the newmodel has avalid H-theoremandcorrectthermal conductivity. We propose Lattice Boltzmann (LB) formulation of this new EnskogBGK model. The molecular nature of the model is verified in case of shear flow by comparing the predicted normal stress behavior by the current model with the prediction of molecular dynamics simulations. We extend the model for multiphase flow by incorporating attractive part as Vlasov type force. To validate multiphase formulation, the results of 3D simulations of a condensing bubble in a periodic box are presented. 

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We propose to extend the d’Humie`res version of the lattice Boltzmann scheme totriangular meshes. We use Bravaislattices or more generallattices with the property that thedegreeof eachinternal vertexis supposedto beconstant. Onsuchmeshes, it is possible todefine the lattice Boltzmannscheme as a discreteparticle method, without need of finite volume formulation or Delaunay-Voronoi hypothesis for the lattice. We test this idea for the heat equation and perform an asymptotic analysis with the Taylor expansion method for two schemes named D2T4 and D2T7. The results show a convergence up to second order accuracy and set new questions concerning a possible super-convergence. 

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As the numerical resolution is increased and the discretisation error decreases, the lattice Boltzmann method tends towards the discrete-velocity Boltzmann equation (DVBE). An expression for the propagation properties of plane sound waves is foundforthisequation. ThisexpressioniscomparedtosimilaronesfromtheNavierStokes and Burnett models, and is found to be closest to the latter. The anisotropy of sound propagation with the DVBE is examined using a two-dimensional velocity set. It is found that both the anisotropy and the deviation between the models is negligible if the Knudsen number is less than 1 by at least an order of magnitude.

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The onset of cavitating conditions inside the nozzle of liquid injectors is known to play a major role on spray characteristics, especially on jet penetration and break-up. In this work, we present a Direct Numerical Simulation (DNS) based on the Lattice Boltzmann Method (LBM) to study the fluid dynamic field inside the nozzle of a cavitating injector. The formation of the cavitating region is determined via a multi-phase approach based on the Shan-Chen equation of state. The results obtained by the LBM simulation show satisfactory agreement with both numerical and experimental data. In addition, numerical evidence of bubble break-up, following upon flow-induced cavitation, is also reported.

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We report about a numerical algorithm based on the lattice Boltzmann method and its applications for simulations of turbulent convection in multi-phase flows. We discuss the issue of ’latent heat’ definition using a thermodynamically consistent pseudo-potential on the lattice. We present results of numerical simulations in 3D with and without boiling, showing the distribution of pressure, density and temperature fluctuations inside a convective cell. 

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Lattice Boltzmann simulations based on the Cahn-Hilliard diffuse interface approachare performed for droplet dynamics in viscous fluid under shear flow, where the degree of confinement between two parallel walls can play an important role. The effects of viscosity ratio, capillary number, Reynolds number, and confinement ratio on droplet deformation and break-up in moderately and highly confined shear flows are investigated.

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We study the static and dynamical behavior of the contact line between two fluids and a solid plate by means of the Lattice Boltzmann method (LBM). The different fluid phases and their contact with the plate are simulated by means of standard Shan-Chen models. We investigate different regimes and compare the multicomponent vs. the multiphase LBM models near the contact line. A static interface profile is attained with the multiphase model just by balancing the hydrostatic pressure (due to gravity) with a pressure jump at the bottom. In order to study the same problem with the multicomponent case we propose and validate an idea of a body force acting only on one of the two fluid components. In order to reproduce results matching an infinite bath, boundary conditions at the bath side play a key role. We quantitatively compare open and wall boundary conditions and study their influence on the shape of the meniscus against static and lubrication theory solution.

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A lattice Boltzmann model for the study of advection-diffusion-reaction (ADR) problems is proposed. Via multiscale expansion analysis, we derive from the LB model the resulting macroscopic equations. It is shown that a linear equilibrium distribution is sufficient to produce ADR equations within error terms of the order of the Mach number squared. Furthermore, we study spatially varying structures arising fromthe interactionof advectivetransportwithacubicautocatalyticreaction-diffusion process under an imposed uniform flow. While advecting all the present species leads to trivial translationof the Turing patterns, differentialadvectionleadsto flow induced instability characterized with traveling stripes with a velocity dependent wave vector parallel to the flow direction. Predictions from a linear stability analysis of the model equations are found to be in line with these observations. 

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A surface based lattice Boltzmann impedance boundary condition (BC) using Ozyoruk’s model [J. Comput. Phys., 146 (1998), pp. 29-57] is proposed and implemented in PowerFLOW. In Ozyoruk’s model, pressure fluctuation is directly linked to normal velocity on an impedance surface. In the present study, the relation between pressure and normal velocity is realized precisely by imposing a mass flux on the surface. This impedance BC is generalized and can handle complex geometry. Combined with the turbulence model in the lattice Boltzmann solver PowerFLOW, this BC can be used to model the effect of a liner in presence of a complex 3D turbulent flow. Preliminary simulations of the NASA Langley grazing flow tube and Kundt tube show satisfying agreement with experimental results. 

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A diesel particulate filter (DPF) is a key technology to meet future emission standards of particulate matters (PM), mainly soot. It is generally consists of a wall-flow type filter positioned in the exhaust stream of a diesel vehicle. It is difficult to simulate the thermal flow in DPF, because we need to consider the soot deposition and combustion in the complex geometry of filter wall. In our previous study, we proposed an approach for the conjugate simulation of gas-solid flow. That is, the gas phase was simulated by the lattice Boltzmann method (LBM), coupled with the equation of heat conduction inside the solid filter substrate. However, its numerical procedure was slightly complex. In this study, to reduce numerical costs, we have tested a new boundary condition with chemical equilibrium in soot combustion at the surface of filter substrate. Based on the soot oxidation rate with catalysts evaluated in experiments, the lattice Boltzmann simulation of soot combustion in the catalyzed DPF is firstly presented to consider the process in the after-treatment of diesel exhaust gas. The heat and mass transfer is shown to discuss the effect of catalysts.

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A finite difference scheme with ghost cell technique is used to study viscous fluid sloshing in 2D and 3D tanks with internal structures. The Navier-Stokes equations in a moving coordinate system are derived and they are mapped onto a time-independent and stretched domain. The staggered grid is used and the revised SIMPLEC iteration algorithm is performed. The developed numerical model is rigorously validated by extensive comparisons with reported analytical, numerical and experimental results. The present numerical results were also validated through an experiment setup with a tank excited by an inclined horizontal excitation or a tank mounted by a vertical baffle. The method is then applied to a number of problems including sloshing fluid in a 2D tank with a bottom-mounted baffle and in a 3D tank with a vertical plate. The phenomena of diagonal sloshing waves affectedby a vertical plate are investigated in detail in this work. The effects of internal structures on the resonant frequency of a tank with liquid are discussed and the present developed numerical method can successfully analyze the sloshing phenomenon in 2D or 3D tanks with internal structures.

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We employ the lattice Boltzmann method and random walk particle tracking tosimulatethetimeevolution ofhydrodynamicdispersioninbulk, random,monodisperse, hard-sphere packings with bed porosities (interparticle void volume fractions) between the random-close and the random-loose packing limit. Using JodreyTory and Monte Carlo-based algorithms and a systematic variation of the packing protocols we generate a portfolio of packings, whose microstructures differ in their degree of heterogeneity (DoH). Because the DoH quantifies the heterogeneity of the void space distribution in a packing, the asymptotic longitudinal dispersion coefficient calculatedforthepackingsincreaseswiththepackings’DoH. Weinvestigatetheinfluence of packing length (up to 150 dp, where dp is the sphere diameter) and grid resolution (up to 90 nodes per dp) on the simulated hydrodynamic dispersion coefficient, and demonstrate that the chosen packing dimensions of 10 dp×10 dp×70 dp and the employed grid resolution of 60 nodes per dp are sufficient to observe asymptotic behavior of the dispersion coefficient and to minimize finite size effects. Asymptotic values of the dispersion coefficients calculated for the generated packings are compared with simulated as well as experimental data from the literature and yield good to excellent agreement.

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This work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies. The fluid flow is modelled by Lattice-Boltzmann Method, coupled to a set of ordinary differential equations describing the dynamics of the solid body in terms its elastic and damping properties. The time discretization of the body dynamicsis performedviatheTime Discontinuous GalerkinMethod. Several numerical examples are presented and highlight the robustness and efficiency of the proposed methodology, by means of comparisons with previously published results. The examples show that the present fluid-structure method is able to capture vortexinduced oscillations of flexibly-supported rigid body. 

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Previous works on impinging streams mainly focused on the structures of flow field, but paid less attention to the structures of temperature field, which are very important in practical applications. In this paper, the influences of the Reynolds number (Re) and Prandtl number (Pr) on the structures of flow and temperature fields of non-isothermal laminar impinging streams are both studied numerically with the lattice Boltzmann method, and two cases with and without buoyancy effect are considered. Numerical results show that the structures are quite different in these cases. Moreover, in the case with buoyancy effect, some new deflection and periodic structures are found, and their independence on the outlet boundary condition is also verified. These findings may help to understand the flow and temperature structures of non-isothermal impinging streams further. 

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A 3D lattice Boltzmann (LB) model with twenty-seven discrete velocities is presented and used for the simulation of three-dimensional porous media flows. Its accuracy in combination with the half-way bounce back boundary condition is assessed. Characteristic properties of the gas diffusion layers that are used in polymer electrolyte fuel cells can be determined with this model. Simulation in samples that have been obtained via X-ray tomographic microscopy, allows to estimate the values of permeability and relative effective diffusivity. Furthermore, the computational LB results are compared with the results of other numerical tools, as well as with experimental values. 

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Lattice-Boltzmannmethods areversatilenumerical modeling techniques capable of reproducing a wide variety of fluid-mechanical behavior. These methods are well suited to parallel implementation, particularly on the single-instruction multiple data (SIMD) parallel processing environments found in computer graphics processing units (GPUs). Although recent programming tools dramatically improve the ease with which GPUbased applications can be written, the programming environment still lacks the flexibility available to more traditional CPU programs. In particular, it may be difficult to develop modular and extensible programs that require variable on-device functionality with current GPU architectures. This paper describes a process of automatic code generation that overcomes these difficulties for lattice-Boltzmann simulations. It details the development of GPU-based modules for an extensible lattice-Boltzmann simulation package – LBHydra. The performance of the automatically generated code is compared to equivalent purpose writtencodesforbothsingle-phase, multiphase, andmulticomponent flows. Theflexibility of the new method is demonstrated by simulating a rising, dissolving droplet moving through a porous medium with user generated lattice-Boltzmann models and subroutines. 

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Fresh water is one of the most significant resources for human activities and survival, and irrigation is among the most important uses of water. The sustainibility and performance of irrigation canals can be greatly affectedby sediment transport and deposition. In our previous works, we proposed a Lattice Boltzmann model for simulating a free surface flow in an irrigation canal, as an alternative to more traditional models mainly based on shallow water equations. Here we introduce the sedimentation phenomenon into our model by adding a new algorithm, based on the earlier work by B. Chopard, A. Dupuis and A. Masselot [9, 11, 12, 27]. Transport, erosion, deposition and toppling of sediments are taken into account and enable the global sedimentation algorithm to simulate different transport modes such as bed load and suspended load. In the present work, we study both the behaviour of a sediment deposit located at an underflow submerged gate (depending on the gate opening and the flow discharge) and the influence of the presence of such a deposit on the flow. Both numerical and experimental validations have been performed. The experiments were realizedon the micro-canalof the LCISlaboratory at Valence, France. The comparisons between simulations and experiments give good qualitative agreement.

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We investigate the hydrodynamic interactions of spherical colloidal nano particles and nano tetrahedra near a planar wall by means of molecular dynamics (MD) simulations of rigid particles within an all-atom solvent. For both spherical and nano-tetrahedral particles, we find that the parallel and perpendicular components of the local diffusion coefficient and viscosity, show good agreement with hydrodynamic theory of Faxe´n and Brenner. This provides further evidence that low perturbations from sphericality of a nanoparticle’s shape has little influence on its local diffusive behaviour, and that for this particular case, the continuum theory fluid dynamics is valid even down to molecular scales.

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Stent placement is considered as a promising and minimally invasive technique to prevent rupture of aneurysm and favor coagulation mechanism inside the aneurysm. Many scholars study the effect of the stent on blood flow in cerebral aneurysm by numerical simulations, and usually regardblood as the Newtonian fluid, blood, however, is a kind of non-Newtonian fluid in practice. The main purpose of the present paper is to investigate the effect of non-Newtonian behavior on the hemodynamic characteristics of blood flow in stented cerebral aneurysm with lattice Boltzmann method. The Casson model is used to describe the blood non-Newtonian character, which is one of the most popular models in depicting blood fluid. In particular, hemodynamic characteristicsderivedwithNewtonianandnon-Newtonianmodelsare studied, and compared in detail. The results show that the non-Newtonian effect gives a great influence on hemodynamic characteristics of blood flow in stented cerebral aneurysm, especially in small necked ones.