Lattice Boltzmann method for fluid dynamics

The lattice Boltzmann method has proven to be a promising method to simulate flow in porous media. Its practical application often relies on parallel computation because of the demand for a large domain and fine grid resolution to adequately resolve pore heterogeneity. The existing domain-decomposition methods for parallel computation usually decompose a domain into a number of subdomains first and then recover the interfaces and perform the load balance. Normally, the interface recovery and the load balance have to be performed iteratively until an acceptable load balance is achieved; this costs time. In this paper we propose a cell-based domain-decomposition method for parallel lattice Boltzmann simulation of flow in porous media. Unlike the existing methods, the cell-based method performs the load balance first to divide the total number of fluid cells into a number of groups ͑or subdomains͒, in which the difference of fluid cells in each group is either 0 or 1, depending on if the total number of fluid cells is a multiple of the processor numbers; the interfaces between the subdomains are recovered at last. The cell-based method is to recover the interfaces rather than the load balance; it does not need iteration and gives an exact load balance. The performance of the proposed method is analyzed and compared using different computer systems; the results indicate that it reaches the theoretical parallel efficiency. The method is then applied to simulate flow in a three-dimensional porous medium obtained with microfocus x-ray computed tomography to calculate the permeability, and the result shows good agreement with the experimental data.

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and noncircular (or/and multiply connected) cross sections where we inspect the flow of Ree-Eyring fluids in tubes of elliptical cross sections. We derive analytical expressions for the flow velocity profile and for the volumetric flow rate. The obtained analytical expressions were tested against the available analytical expressions for the special cases of Newtonian flow in circular tubes, Newtonian flow in elliptical tubes and Ree-Eyring flow in circular tubes and the results were identical. The obtained analytical expressions were also tested for sensible trends, tendencies and correlations and they passed all these tests.

One form of numerical simulation of flow and particle capture by air filter media sees gases as continuous fluids, influenced by
the macro-properties viscosity, density, and pressure. The alternate approach treats gases as atoms or molecules in random motion,
impacting their own kind and solid surfaces on a micro-scale. The appropriate form for analysis of flow through a given filter medium
at a given operating condition depends on the gas condition and the Knudsen number (Kn) of the finest fibers in the filter medium
simulated. Continuum, macro-scale methods may be usable for media with individual fiber Kn as high as 0.01. Part I of this article
discussed simulations of air filter media performance, where all fibers are in the continuum flow regime and the Navier–Stokes
equation with a finite-volume solution is applicable. Here, Part II discusses filter media performance simulation by computational
approaches other than numerical solutions of the Navier–Stokes equation. These include use of the Burnett, super-Burnett, and
Grad moment equations; lattice Boltzmann and direct simulation Monte Carlo methods; and the molecular dynamics, boundary
singularity, and boundary element methods.

In this paper, we propose a lattice Boltzmann model for coupled Burgers equations (CBEs). With a proper time-space scale and the Chapman-Enskog expansion, the governing equations are recovered successfully from the lattice Boltzmann equations, and the resulting local equilibrium distribution functions are also obtained. The partial derivative ∂(uv)/∂x in the model is treated as a source term and discretized with a 2nd-order central difference scheme. Numerical experiments show that the numerical results by the Lattice Boltzmann Method (LBM) either agree well with the corresponding exact solutions or are quite comparable with those available numerical results in the literature.

Nuclear engineering requires computationally efficient methods to simulate different components and systems of plants. The Lattice Boltzmann Method (LBM), a numerical method with a mesoscopic approach to Computational Fluid Dynamic (CFD) derived from the Boltzmann equation and the Maxwell–Boltzmann distribution, can be an adequate option. The purpose of this paper is to present a review of the recent applications of the Lattice Boltzmann Method in nuclear engineering research. A systematic literature review using three databases (Web of Science, Scopus, and ScienceDirect) was done, and the items found were categorized by the main research topics into computational fluid dynamics and neutronic applications. The features of the problem addressed, the characteristics of the numerical method, and some relevant conclusions of each study are resumed and presented. A total of 45 items (25 for computational fluid dynamics applications and 20 for neutronics) was found on a wide range of nucl...

The effects of ice accretion on the aerodynamic performance of a naca0012 airfoil are investigated numerically using a Two-dimensional unsteady compressible Lattice Boltzmann method (LBM). The ice shape is obtained from an empirical model based on experimental data. The flow conditions are chosen to represent typical icing conditions encountered by aircraft at low and moderate Reynolds numbers. The simulations are performed for different angles of attack and ice shapes to study the influence of icing on the lift, drag, and moment coefficients, as well as the flow structures and separation behavior. The results show that icing reduces the lift and increases the drag and pitching moment of the airfoil, and also induces earlier flow separation and larger wake regions. The severity of these effects depends on the ice shape, angle of attack, and Reynolds number. The present study provides valuable insights into the physics of iced airfoil flows and can be useful for improving the design and safety of aircraft operating in icing environments.

The three-dimensional thermal lattice Boltzmann-BGK model is developed to simulate the pressure-driven rarefied gaseous flow within a circular channel with constant-temperature-wall in the transition regime (0.1 <Kn<1). The D3Q15 model has been employed for velocity discretization. The captured nonlinear behavior of gas in the Knudsen layer, which dominates the flow characteristics in small-scale gaseous flows by modifying the near-wall correction function along with the variation of properties with density and temperature distributions are implemented in a new formulation. An appropriate combination of advanced straight boundary conditions and a 3D extension of an available curved boundary conditions by identifying the nodes either adjacent to the solid nodes or flow nodes on the computational domain with the structured mesh are employed. The results of small-scale phenomena such as slip-velocity and temperature-jump are reported, which are manifestations of the cases with non-zero Knudsen number. Due to the deficiency of the continuum presumption for high-Knudsen flows, the present study suggests that the TLBM is an efficient tool applicable to the theoretical development of low speed gas flow study, which typically falls within the realm of MEMS/ NEMS by virtue of its more straightforward boundary treatments and higher computation capability compared to other atomistic approaches.

Granular column collapses show a significant size effect with respect to run-out distances and phase transitions; • The size effect can be further associated with the strong force networks and earlystage characteristic length scales; • We draw similarities between granular column collapses and dome-collapse pyroclastic flows.

Friction is a fundamental force that governs interactions across diverse physical systems, influencing motion, energy transfer, and material behavior. This article provides an in-depth exploration of the various types of friction-static, kinetic, rolling, and fluid-and their intricate interplay within the realms of physics, engineering, biology, and environmental science. By examining the coefficient of friction, surface roughness, and energy dissipation, we elucidate how frictional forces are not merely resistive but also enable critical functions, such as propulsion in transportation, stability in structural design, and efficiency in mechanical systems. Additionally, the role of friction in human biomechanics highlights its significance in motion and ergonomics, demonstrating its relevance to health sciences. Through an interdisciplinary lens, we reveal that friction is integral to the design and optimization of technologies ranging from everyday appliances to advanced engineering applications. Ultimately, this comprehensive analysis underscores the necessity of understanding friction's multifaceted role, fostering innovative solutions that harness its properties for improved performance and sustainability in both natural and engineered systems.

Les equations de Navier-Stockes en leur forme complete sont tres compliquees du fait de la presence des termes non lineaires. La resolution de ces equations exige des hypotheses specifiques pour chaque situation. Dans cette contribution, on essayera d’etudier l’ecoulement non stationnaire d’un fluide incompressible dans un domaine cartesien en presence d’un gradient de pression. L’etude portera sur l’effet du temps et du gradient de pression sur l’evolution de la vitesse d’ecoulement. Pour resoudre le probleme, les methodes analytiques et numeriques seront utilisees.

Numerical solutions of 2-D laminar flow over a backwardfacing step using the lattice Boltzmann equation method (LBEM) are presented in this article. Unlike conventional numerical schemes based on macroscopic continuum equation (mass conservation and Navier-Stokes) discretisation, the LBEM is based on microscopic models and mesoscopic kinetic equations. The simulations were validated for a wide range of Reynolds numbers (100 ≤ Re ≤ 1,000), comparing them to previous studies. Several flow features, such as primary and secondary vortex location at the bottom and top of the wall, respectively, were investigated regarding Reynolds number. Two typical classes of boundary condition were implemented in the LBEM model: the Drichlet condition at the inlet flow (parabolic speed profile) and the Newman condition at the outlet flow (zero gradient speed). The results showed that the LBEM gave accurate results over a wide range of Reynolds number; these were compared with other numerical methods and experimental data.

The finite element method is applied to the one-dimensional neutron transport equation. Piecewise bilinear or trilinear polynomials that are continuous in the space-angle phase space are utilized in an even-parity functional for the angular flux to establish linear simultaneous sets of algebraic equations. Both inhomogeneous and eigenvalue problems in slab, spherical, and cylindrical geometries are treated. The application of the finite element method to problems with anisotropic scattering and material interfaces is also demonstrated. In all cases, the accuracy of the finite element results is an improvement over that obtained from standard S N calculations using comparable numbers of simultaneous equations.

Simulation technologies are applied extensively in casting industries to understand the heat transfer and fluid transport phenomena and their relationships to the microstructure and the formation of defects. It is critical to have accurate thermo-physical properties as input for reliable simulations of the complex solidification and solid phase transformation processes. The thermo-physical properties can be calculated with the help of thermodynamic calculations of phase stability at given temperatures and compositions. A multicomponent alloy solidification model, coupled with a Gibbs free energy minimization engine and thermodynamic databases, has been developed. A back diffusion model is integrated so that the solidification conditions, such as cooling rate, can be taken into account.

Transport de contaminant dans un milieu poreux -- Les équations de base -- Solution numérique -- Schéma non oscillatoire avec évaluation exacte du front -- Étude numérique des transferts bidimensionnels dans la zone non saturée, application à l&#39;étude du drainage et de la recharge d&#39;une nappe à surface libre -- Modélisation de la migration d&#39;un contaminant dense dans un milieu poreux saturé -- Transport d&#39;un panache à plusieurs éléments contaminants dans un écoulement à densité variable -- Modélisation de la migration de contaminant dans le site d&#39;enfouissement Borden en Ontario -- Champs d&#39;application de la méthode EPCOF

A time-domain method for acoustic propagation and its application to tone noise radiated from rigid-wall fan inlets are presented. The noise propagation phenomena are modeled by the nonlinear time-dependent Euler equations written in conservative form. The equations are solved numerically using a staggered-grid multidomain Chebyshev discretization for the spatial terms and a Runge-Kutta scheme for time integration. Various types of radiation boundary conditions are implemented and investigated on generic benchmarks. The resulting code is optimized on parallel machines with shared memory. The method is rst validated on noise radiation from twodimensional and axisymmetric at ducts with no mean ow for which analytical data exist. The full potential of the method is then tested by computing the sound eld radiated from an axisymmetric bell-mouth duct in a nonuniform mean ow. Three-dimensional computations of the sound eld in a bent pipe, on which both experiments and computations using a boundary integral method have been carried out at ONERA, are also presented.

A Rayleigh Bénard instability study using the energy conserving dissipative particle dynamics method is presented here for the first time. The simulation is performed on an ideal dissipative particle dynamics fluid in a three dimensional domain with carefully selected parameters to make the convection terms in the equation more dominant than the conduction ones. Beyond a critical temperature difference a two cell pattern is observed as the dominant structure. As the temperature is increased further, the density changes in the system are sharp with formation of distinct high density layers close to the cold wall. Doubling the length of the domain led to the formation of four convection cells with the same cell diameter as before, confirming the invariance of the pattern formation in that dimension. Changes in the height of the domain led to cells with more uniform looking patterns. The results and patterns seen here are qualitatively similar to previous studies performed on rarefied gases.

Mixed convection heat and mass transfer of a hybrid nanofluid in a lid-driven irregular hexagon cavity is numerically studied in this paper. The nanofluid is composed of the multi-walled carbon nanotube and the magnesium oxide (MgO) nanoparticles (15-85 vol%) dispersed in a non-Newtonian carboxymethyl cellulose-based fluid obeying the Ostwald-de Waele rheological model. The governing equations are solved numerically by means of the finite volume method and the SIMPLER algorithm to treat the velocity-pressure coupling. The study is performed for some relevant physical parameters: the Richardson number (Ri = 0.001-10), the power law index (n = 0.2-1.0), the buoyancy ratio (N = − 3 to + 3), and the total solid volume fraction (φ = 0.0-0.02). The obtained results are presented in terms of streamlines, isotherms, isoconcentrations, velocity profiles, and local and average Nusselt and Sherwood numbers. This work proves the significant impact of the quoted parameters on the hydrodynamic, thermal, and mass fields. Indeed, the flow structure is more sensitive to the power law index and the Richardson number variations. Moreover, heat and mass transfer are enhanced by the decline of the latter. Also, the addition of nanoparticles enhances heat transfer for the three convection modes especially for the dominant forced convection mode (Ri = 0.001) where the improvement reaches 14.42% for a power law index equal to 0.8. However, it improves mass transfer in the dominant forced convection but in mixed and dominant natural convection (Ri = 1, 10) as the buoyancy ratio equal to + 2 and + 3. Keywords Mixed convection • Thermosolutal • Lid-driven irregular hexagon cavity • MWCNT-MgO/CMC non-Newtonian hybrid nanofluid • Finite volume method List of symbols c p Heat capacity (J kg −1 K −1) C Concentration (kg m −3) D Mass diffusivity (m 2 s −1) g Gravitational acceleration (m s −2) Gr Grashof number k Thermal conductivity (W m −1 K −1) K Consistency coefficient (Pa s n) L Length of the cavity (m) Le Lewis number n Power law index N Buoyancy ratio Nu Nusselt number Nu avg Average Nusselt number p Pressure (Pa) P Dimensionless pressure Pr Prandtl number Re Reynolds number Ri Richardson number S Dimensionless coordinate adopted for distance along the inclined walls Sh Sherwood number Sh avg Average Sherwood number T Temperature (K) u, v Velocity components (m s −1) U, V Dimensionless velocity components x, y Cartesian coordinates (m) X, Y Dimensionless Cartesian coordinates Greek letters α Thermal diffusivity (m 2 s −1) β Thermal expansion coefficient (K −1) Shear rate (s −1)

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Nuclear engineering requires computationally efficient methods to simulate different components and systems of plants. The Lattice Boltzmann Method (LBM), a numerical method with a mesoscopic approach to Computational Fluid Dynamic (CFD) derived from the Boltzmann equation and the Maxwell–Boltzmann distribution, can be an adequate option. The purpose of this paper is to present a review of the recent applications of the Lattice Boltzmann Method in nuclear engineering research. A systematic literature review using three databases (Web of Science, Scopus, and ScienceDirect) was done, and the items found were categorized by the main research topics into computational fluid dynamics and neutronic applications. The features of the problem addressed, the characteristics of the numerical method, and some relevant conclusions of each study are resumed and presented. A total of 45 items (25 for computational fluid dynamics applications and 20 for neutronics) was found on a wide range of nucl...

In this article, we present a predictive model for the amplitude of impulse waves generated by the collapse of a granular column into a water layer. The model, which combines the spreading dynamics of the grains and the wave hydrodynamics in shallow water, is successfully compared to a large dataset of laboratory experiments, and captures the influence of the initial parameters while giving an accurate prediction. Furthermore, the role played on the wave generation by two key dimensionless numbers, i.e., the global Froude number and the relative volume of the immersed deposit, is rationalized. These results provide a simplified, yet comprehensive, physical description of the generation of tsunami waves engendered by large-scale subaerial landslides, rockfalls, or cliff collapses in a shallow water.

The overall aim intended of the present work is to simulate an incompressible laminar flow and thermal transfer in a constricted channel. A double multiple relaxation time (DMRT) thermal lattice Boltzmann method is carried out on this problem. The application of this method will be performed using a multiple relaxation time D2Q9 and D2Q5 model to simulate numerically the flow field and the thermal field, respectively. This paper deals with various interesting features of the flow and temperature fields in the constricted channel to describe the fluid behavior. Furthermore, the effects of several parameters (Reynolds number, height of constricted part...) were studied and discussed in detail in order to find some improvements about the heat transfer mechanism in the presence of the constricted part.

We study the effect of adsorbed surfactant on drop deformation in linear flows by means of analytical solutions for small perturbations of the drop shape and surfactant distribution, and by numerical simulations for large distortions. We consider a drop with the same viscosity as the suspending fluid. Under these conditions, the problem simplifies because the disturbance flow field results solely from the interfacial stresses that oppose the distortion of shape and surfactant distribution induced by the incident flow. A general form of perturbation analysis valid for any flow is presented. The analysis can be carried out to arbitrary order given its recursive structure; a third-order perturbation solution is explicitly presented. The expansions are compared to results from boundary integral simulations for drops in axisymmetric extensional and simple shear flows. Our results indicate that under weak-flow conditions, deformation is enhanced by the presence of surfactant, but the leading-order perturbation of the drop shape is independent of the ͑nonzero͒ surfactant elasticity. In strong flows, drop deformation depends nonmonotonically on surfactant elasticity. The non-Newtonian rheology in a dilute emulsion that results from drop deformation and surfactant redistribution is predicted. Shear thinning is most pronounced for low values of the surfactant elasticity. In the weak-flow limit with finite surfactant elasticity, the emulsion behaves as a suspension of rigid spheres. In strong flows, the stresses can approach the behavior for surfactant-free drops.

The Meshless Lattice Boltzmann Method (MLBM) is a numerical tool that relieves the standard Lattice Boltzmann Method (LBM) from regular lattices and, at the same time, decouples space and velocity discretizations. In this study, we investigate the numerical convergence of MLBM in three benchmark tests: the Taylor-Green vortex, annular (bent) channel and a porous medium flow. We compare our MLBM results to LBM and to the analytical solution of the Navier-Stokes equation. We investigate the method's convergence in terms of the discretization parameter, the interpolation order, and the LBM streaming distance refinement. We observe that MLBM outperforms LBM in terms of the error value for the same number of nodes discretizing the domain. We find that LBM errors at a given streaming distance and timestep length are the asymptotic lower bounds of MLBM errors with the same streaming distance and timestep length. Finally, we suggest an expression for the MLBM error that consists of the LBM error and other terms related to the semi-Lagrangian nature of the discussed method itself.

Le phénomène connu sous le nom de "tuyau chantant" concerne l'émission acoustique de tuyaux qui peuvent se mettre à siffler lorsqu'ils sont soumis à un écoulement interne de gaz. Ce sifflement trouve son origine dans la géométrie particulière de ces tuyaux qu'on qualifie de "corrugués" parce que leur paroi interne est constituée d'une suite de cavités régulièrement espacées. Afin de prédire ce sifflement, il est important de comprendre les mécanismes qui sont à l'origine de l'émission sonore. L'étude s'appuie sur une approche numérique en DNS par la méthode Lattice-Boltzman (LBM) confrontée à des résultats expérimentaux. Une expérience de tuyau corrugué chantant a été montée à IRPHE autour d'un tuyau rectangulaire transparent de longueur L = 2m. Les corrugations sont de dimension caractéristique de 10mm. L'écoulement a été caractérisé par des mesures de vitesse et de pression acoustique jusqu'à des vitesses de 25m/s. Une analyse de la dynamique des structures de la turbulence qui se développent dans les couches cisaillées de l'écoulement a été réalisée par la méthode d'estimation stochastique linéaire (LSE). Nous avons observé que ce sifflement trouve son origine dans le couplage entre les mouvements de la couche de cisaillement qui se développe sur les parois du tuyau et les modes acoustiques du tuyau. Le rôle des premières corrugations ayant été exploré expérimentalement, le modèle numérique permet d'étendre cette observation à tout le tuyau corrugué, et d'explorer les contributions des différentes régions de l'écoulement à l'émission sonore. Le modèle utilise le code libre Palabos, basé sur la LBM. Cette méthode numérique donne accès à un grand nombre de paramètres en tous points de la géométrie et permet d'observer les fluctuations de pression et de les corréler avec l'écoulement. La complémentarité des approches expérimentale et numérique apporte des éléments de compréhension des mécanismes de génération du sifflement dans les tuyaux corrugués.

A butterfly with broad wings, flapping at a small frequency, flies an erratic trajectory at an inconstant speed. A large variation of speed within a cycle is observed in the forward flight of a butterfly. A self-propulsion model to simulate a butterfly is thus created to investigate the transient translation of the body; the results, which are in accordance with experimental data, show that the shape of the variation of the flight speed is similar to a sinusoidal wave with a maximum (J=0.89) at the beginning of the downstroke, and a decrease to a minimum (J=0.17) during a transition from downstroke to upstroke; the difference between the extrema of the flight speed is enormous in a flapping cycle. At a high speed, a clapping motion of the butterfly wings decreases the generation of drag. At a small speed, a butterfly is able to capture the induced wakes generated in a downstroke, and effectively generates a thrust at the beginning of an upstroke. The wing motion of a butterfly skill...

This paper investigates forced convection of water/Al 2 O 3 nanofluid flow in a microchannel with inclined cross-flow injection on the lower wall. There are a number of injecting holes on its lower wall. Other walls are insulated. The effect of different parameters including injection angle and number of injections on slip flow and heat transfer is investigated. It is concluded that increasing the injection angle up to 94° lead to an enhancement of the slip velocity and the Nusselt number on the microchannel walls. The results demonstrate that maximum heat transfer corresponds to the injection angle of 94°. It is revealed that the variation of Nusselt number decreases with the number of injection. As the volume fraction of nanoparticles increases, the heat transfer rate increases.

In this study, forced convection heat transfer of water/alumina Nano fluid in a rectangular microchannel with cross-flow injection is studied. The Nano fluid enters the microchannel with a temperature of 293 K and cools its walls. The upper wall of the microchannel is at constant temperature of 303 K. On the lower wall, there are two holes for injection of Nano fluid flow. Other parts of the microchannel wall are insulated. Slip velocity boundary condition is used for the walls of the microchannel. Simulations are performed for different injection velocities and the results are presented as velocity and temperature fields, and variation of the Nusselt number. The results show that the slip velocity on the channel wall and the Nusselt number increase by increasing the injection velocity. It is revealed that the Nusselt number is maximum at the channel entrance and decreases along the channel. After each injection, local Nusselt number increases due to the increase of the temperature gradient in the microchannel. Moreover, an optimal value for the ratio of the injection velocity to the inlet velocity is achieved using performance evaluation criteria (PEC). It is concluded that ⁄ = 10 is an optimal value of the injection velocity, leading to maximum PEC.

Application of the lattice Boltzmann method (LBM) to solve the energy equations of conduction-radiation problems is extended on non-uniform lattices. In the LBM on non-uniform lattices, the single relaxation time based on the minimum velocity is used. This minimum velocity corresponds to the smallest size lattice. Because information propagates with the same minimum velocity in the prescribed directions from all the lattice centers, in a given time step, they are not equidistant from the neighboring lattices. Collisions in the LBM take place at the same instant. Therefore, in the LBM on non-uniform lattices, in every time step, interpolation is required to carry the information to the neighboring lattice centers. To validate this very concept in heat transfer problems involving thermal radiation, transient conduction and radiation heat transfer problems in a 1-D planar and a 2-D rectangular geometries containing absorbing, emitting and scattering medium are considered. The finite volume method (FVM) is used to compute the radiative information. In both the geometries, results for the effects of various parameters are compared for LBM-FVM on uniform and non-uniform lattices. To establish the LBM-FVM on non-uniform lattices for the combined conduction and radiation heat transfer problems, numerical experiments were performed with different cluster values. The accurate results were found in all the cases.

Application of the lattice Boltzmann method (LBM) to solve the energy equations of conduction-radiation problems is extended on non-uniform lattices. In the LBM on non-uniform lattices, the single relaxation time based on the minimum velocity is used. This minimum velocity corresponds to the smallest size lattice. Because information propagates with the same minimum velocity in the prescribed directions from all the lattice centers, in a given time step, they are not equidistant from the neighboring lattices. Collisions in the LBM take place at the same instant. Therefore, in the LBM on non-uniform lattices, in every time step, interpolation is required to carry the information to the neighboring lattice centers. To validate this very concept in heat transfer problems involving thermal radiation, transient conduction and radiation heat transfer problems in a 1-D planar and a 2-D rectangular geometries containing absorbing, emitting and scattering medium are considered. The finite volume method (FVM) is used to compute the radiative information. In both the geometries, results for the effects of various parameters are compared for LBM-FVM on uniform and non-uniform lattices. To establish the LBM-FVM on non-uniform lattices for the combined conduction and radiation heat transfer problems, numerical experiments were performed with different cluster values. The accurate results were found in all the cases.

In this paper, a finite volume lattice Boltzmann method (FVLBM) based on cell-center unstructured girds is presented and full studied to simulate the incompressible laminar flows, which is simple modified from the cell-vertex unstructured girds FVLBM proposed by Stiebler et al.

In this study, the heat transfer and laminar flow of Water/Al 2 O 3 nanofluid in a T-shaped enclosure with lid-driven under the influence of applying magnetic field have been numerically investigated. The numerical solving domain has been simulated two-dimensionally for Richardson numbers of 0.1, 1 and 10 for volume fractions of 0-6% of nanoparticles. In this paper, the effect of applying homogeneous magnetic field in Hartman numbers of 0, 30 and 60 on the natural and forced heat transfer parameters of nanofluid has been analyzed and compared. The results of this research revealed that, applying magnetic field has significant effect on the temperature domain and fluid flow and considerably reduces the circulation mechanisms of fluid. By increasing Richardson and Hartmann numbers, the transfer momentum of cap in the bottom layers of fluid penetrates lesser and the amount of heat transfer reduces. The enhancement of volume fraction of nanoparticles and the reduction of Richardson and Hartmann numbers, significantly enhance the heat transfer of enclosure with cold fluid. Also, the changes of volume fraction of nanoparticles have less influence on the variations of velocity domain and the changes of magnetic field intensity greatly affect the velocity domain.

Suspensions of micron size particles form a large class of multi-physics problems and find applications in, e.g., microfluidic devices [1], additive manufacturing [2] and pharmaceutical industry [3]. In this work, we study such suspensions using the discrete element method (DEM) coupled with a kinetic theory based lattice Boltzmann method (LBM) [4] to resolve particle dynamics and multiple fields, e.g., fluid or electric-field, respectively. Position updates of each particle computed in DEM at a given time are communicated to the LBM algorithm through a DEM-LBM interface. Here, we use sophisticated extrapolation methods to transfer the particle-centric information of DEM to the computational grid-level information for the LBM and vice versa. Coupling of DEM and LBM has only very recently been examined [5,6]. The design of this interface is important to obtain time accurate results. The present work details on the analysis of particle suspension in viscous fluid (such as dielectric f...

In this work, minimal kinetic theories based on unconventional entropy functions, H ∼ lnf (Burg entropy) for 2D and H ∼ f 1− 2 n (Tsallis entropy) for nD with n 3, are studied. These entropy functions were originally derived by Boghosian et al. [Phys. Rev. E 68, 025103 (2003)] as a basis for discrete-velocity and lattice Boltzmann models for incompressible fluid dynamics. The present paper extends the entropic models of Boghosian et al. and shows that the explicit form of the equilibrium distribution function (EDF) of their models, in the continuous-velocity limit, can be identified with the Poisson kernel of the Poisson integral formula. The conservation and Navier-Stokes equations are recovered at low Mach numbers, and it is shown that rest particles can be used to rectify the speed of sound of the extended models. Fourier series expansion of the EDF is used to evaluate the discretization errors of the model. It is shown that the expansion coefficients of the Fourier series coincide with the velocity moments of the model. Employing two-, three-, and four-dimensional (2D, 3D, and 4D) complex systems, the real velocity space is mapped into the hypercomplex spaces and it is shown that the velocity moments can be evaluated, using the Poisson integral formula, in the hypercomplex space. For the practical applications, a 3D projection of the 4D model is presented, and the existence of an H theorem for the discrete model is investigated. The theoretical results have been verified by simulating the following benchmark problems: (1) the Kelvin-Helmholtz instability of thin shear layers in a doubly periodic domain and (2) the 3D flow of incompressible fluid in a lid-driven cubic cavity. The present results are in agreement with the previous works, while they show better stability of the proposed kinetic model, as compared with the BGK type (with single relaxation time) lattice Boltzmann models.

Une étude numérique tridimensionnelle a été menée pour déterminer les effets du rapport de forme transverse, A y , sur la structure générale de l'écoulement au sein d'une cavité entraînée. La méthode numérique est basée sur une formulation de type volumes finis et une accélération multigrille. Pour un nombre de Reynolds fixe Re = 1000, quatre rapports de forme A y = 1, 0,5, 0,25 et 0,125 ont été envisagés. Des lignes de courant dans le plan médian sont présentées, relativement aux différents rapports de forme transverses considérés, montrant la complexité de l'écoulement lorsque A y devient faible. On note également que la diminution du rapport de forme entraîne une nette diminution de la transmission de l'énergie cinétique fournie par la paroi d'entraînement vers le fond de la cavité.

La mécanique des fluides décrit des phénomènes physiques des fluides qui sont souvent gouvernés par des équations de type dérivées partielles à savoir l'équation de continuité et l'équation de Navier-Stokes. La résolution de ces équations en utilisant des méthodes classiques rencontre certaines difficultés lorsqu'il s'agit de traiter des problèmes où la géométrie du milieu est complexe ou lorsqu'on se trouve en présence de plusieurs phases d'un fluide ou de plusieurs fluides [TAO 16]. La tendance actuelle s'oriente vers une nouvelle approche pour la recherche en simulation [CFD], qui a gagné beaucoup de popularité ces dernières années, elle est appelée en anglais « Lattice Boltzmann Method » (LBM), qui est un développement relativement nouveau dans la CFD. La méthode de Lattice-Boltzmann est une méthode de dynamique des fluides (CFD). À la place des équations de Navier-Stokes, l'équation discrète de Boltzmann est résolue pour simuler le comportement de fluides à l'aide d'un schéma de collision-propagation. Dans ce travail, on a intégré la LBM dans un code python afin de simuler en 2D le comportement d'un fluide en charge à l'encontre d'un obstacle, chose qui va nous servir par la suite à déterminer dans les conduites les zones les plus sollicités (vitesse maximale et pression maximale) pour mieux dimensionner à la fois la conduite et ses accessoires (vanne, clapet, etc.) et éviter leur dégradation rapide. ABSTRACT. Fluid mechanics describes the physical phenomena of fluids which are often governed by partial derivative equations namely the continuity equation and the Navier-Stokes equation. The resolution of these equations using conventional methods encounters certain difficulties when it comes to dealing with problems where the geometry of the medium is complex or when there are several phases of a fluid or several fluids [TAO 16]. The current trend is towards a new approach to simulation research [CFD], which has gained a lot of popularity in recent years, it is called in English "Lattice Boltzmann Method" (LBM), which is a relatively new development in the Computational fluid dynamics [CFD]. The lattice Boltzmann method is a method of fluid dynamics (CFD). Instead of the Navier-Stokes equations, the Boltzmann discrete equation is solved to simulate the behavior of fluids using a collision-propagation scheme. In this work, the LBM was integrated in a python code in order to simulate in 2D the behavior of a pipe flow against an obstacle, which will be used later to determine in the pipes the most solicited zones (maximum velocity and maximum pressure) to better size both the pipe and its accessories (valve, etc.) and prevent their rapid degradation. MOTS-CLÉS. Ecoulement en charge, Simulation,

In this work we explore the possibility of learning from data collision operators for the Lattice Boltzmann Method using a deep learning approach. We compare a hierarchy of designs of the neural network (NN) collision operator and evaluate the performance of the resulting LBM method in reproducing time dynamics of several canonical flows. In the current study, as a first attempt to address the learning problem, the data was generated by a single relaxation time BGK operator. We demonstrate that vanilla NN architecture has very limited accuracy. On the other hand, by embedding physical properties, such as conservation laws and symmetries, it is possible to dramatically increase the accuracy by several orders of magnitude and correctly reproduce the short and long time dynamics of standard fluid flows.

A new solver for second-order elliptic partial differential equations (PDEs) based on the lattice Boltzmann method (LBM) and the multigrid (MG) technique is presented. Several benchmark elliptic equations are solved numerically with the inclusion of multiple grid-levels in two-dimensional domains at an optimal computational cost within the LB framework. The results are compared with the corresponding analytical solutions and numerical solutions obtained using the Stone's strongly implicit procedure. The classical PDEs considered in this article include the Laplace and Poisson equations with Dirichlet boundary conditions, with the latter involving both constant and variable coefficients. A detailed analysis of solution accuracy, convergence and computational efficiency of the proposed solver is given. It is observed that the use of a high-order stencil (for smoothing) improves convergence and accuracy for an equivalent number of smoothing sweeps. The effect of the type of scheduling cycle (V-or W-cycle) on the performance of the MG-LBM is analyzed. Next, a parallel algorithm for the MG-LBM solver is presented and then its parallel performance on a multi-core cluster is analyzed. Lastly, a practical example is provided wherein the proposed elliptic PDE solver is used to compute the electro-static potential encountered in an electro-chemical cell, which demonstrates the effectiveness of this new solver in complex coupled systems. Several orders of magnitude gains in convergence and parallel scaling for the canonical problems, and a factor of 5 reduction for the multiphysics problem are achieved using the MG-LBM.

Certainly, here is the corrected version with spelling and grammar errors addressed:

"A numerical simulation of heat transfer and pressure loss analysis is presented for variously shaped turbulators inserted into a rectangular channel. A constant heat flux is applied to the external side of the channel. Numerical simulations were conducted using COMSOL Multiphysics. The shapes of the turbulators vary, and the effects of turbulator height are studied.

The obtained numerical results clearly show that the dynamic and thermal performances depend on the dimensions and shape of the turbulators. The development of swirling structures behind the turbulators is observed, which seems to be responsible for the increase in heat transfer. Pressure drops are primarily attributed to the flow blockage caused by these elements."

Given a planar potential V, we look for families of orbits f(x,y)=c% (determined by their slope function gamma=f_{y}/f_{x}), traced by a material point of unit mass under the action of that potential. The second-order equation which relates gamma and V is nonlinear in gamma; to find special solutions, we consider in addition a linear first-order partial differential equation satisfied by gamma. The problem does not admit always solutions; but when solutions do exist, they can be found by algebraic manipulations. Examples are given for homogeneous families gamma, and for some special cases which arise in the course of reasoning.

In many earth science and environmental problems, the fluid-structure interactions can affect the hydrodynamics properties of the porous medium via the spatial evolution of its solid matrix. A significant insight into these properties can be obtained from pore-scale simulations. Using a 3D pore-scale domain with moving walls, we proposed in this paper a comparison of the numerical accuracy between different approaches in regard to flow and reactive transport. Two direct-forcing immersed boundary (IB) models coupled with lattice Boltzmann method (LBM) are evaluated for the flow calculation against an analytical solution. The IB-LBM showed improvement compared to the classical and interpolated bounce-back lattice Boltzmann model. Concerning the reactive transport, the most accurate IB-LB method was coupled with two non-boundary conforming finite volume methods (volume of fluid and reconstruction). The comparative study performed with different mesh sizes and Damköhler numbers demonstrates better results for the reconstruction method. Keywords Lattice Boltzmann • Immersed boundary method • Reconstruction method • Volume of fluid • Porous medium List of symbols c Lattice speed c f , c r Solute concentrations in Ω f , Ω r c s Speed of sound Da Damköhler number

Les equations de Navier-Stockes en leur forme complete sont tres compliquees du fait de la presence des termes non lineaires. La resolution de ces equations exige des hypotheses specifiques pour chaque situation. Dans cette contribution, on essayera d’etudier l’ecoulement non stationnaire d’un fluide incompressible dans un domaine cartesien en presence d’un gradient de pression. L’etude portera sur l’effet du temps et du gradient de pression sur l’evolution de la vitesse d’ecoulement. Pour resoudre le probleme, les methodes analytiques et numeriques seront utilisees.

We study the influence of a low frequency vibration on a long-wave Marangoni convection in a layer of a binary mixture with the Soret effect. A linear stability analysis is performed numerically by means of the Floquet theory; several limiting cases are treated analytically. Competition of subharmonic, synchronous, and quasiperiodic modes is considered. The vibration is found to destabilize the layer, decreasing the stability threshold. Also, a vibration-induced mode is detected, which takes place even for zero Marangoni number.

Generalized finite difference methods require that a properly posed set of nodes exists around each node in the mesh, so that the solution for the corresponding multivariate interpolation problem be unique. In this paper we first show that the construction of these meshes can be computerized using a relatively simple algorithm based on the concept of a Coatmèlec lattice. Then, we present a generalized finite difference method which provides a numerical solution of a partial differential equation over an arbitrary domain, using the generated meshes. The accuracy and mesh adaptivity of the method is evaluated using elliptical equations in several domains.

A two dimensional (2D) cellular automaton (CA) - lattice Boltzmann (LB) model is presented to investigate the effects of forced melt convection on the solutal dendritic growth. In the model, the CA approach of simulating the dendritic growth is incorporated with the kinetic-based lattice Boltzmann method (LBM) for numerically solving the melt flow and solute transport. Two sets of distribution functions are used in the LBM to model the convective-diffusion phenomena during dendritic growth. After validating the model by comparing the numerical results with the theoretical solutions, it is applied to simulate the single and multi dendritic growth of Al - Cu alloys without and with a forced convection. The typical asymmetric growth features of convective dendrite are reproduced and the dendritic morphology is strongly influenced by melt convection. The simulated convective multi dendritic features by the present model are also compared with that by the CA-NS model. The present model i...

A two-dimensional lattice Boltzmann-cellular automaton model is coupled with the CALPHAD (Calculation of Phase Diagrams) method for simulating dendritic growth during ternary alloy solidification with convection. In the model, the kinetics of dendritic growth is determined by the difference between the equilibrium liquidus temperature and the actual temperature at the solid/liquid interface, incorporating the effects of the interface curvature and the preferred dendritic growth orientation. The lattice Boltzmann method is used for evaluating the local liquid compositions of the two solutes impacted by diffusion and convection. Based on the local liquid compositions, the equilibrium liquidus temperature and the solid concentrations of the two solutes are obtained by the CALPHAD method. The model is applied to simulate dendritic growth of an Al-4?0 wt-%Cu-1?0 wt-%Mg ternary alloy with melt convection. The results demonstrate the high numerical convergence and stability, as well as computational efficiency, of the proposed model. Melt convection is found to influence the dendritic morphologies and microsegregation patterns in the solidification of ternary alloys.

In this study, we present a numerical simulation of MWCNT-Fe 3 O 4 /water hybrid nanofluid forced convection heat transfer over the forward-and backward-facing steps channel having a baffle fixed on its top wall. A FORTRAN's homemade code based the lattice Boltzmann method (LBM) is used here. The effects of the Reynolds number (25 ≤ Re ≤ 100), the volume fraction of nanoparticles (0 ≤ φ ≤ 0.003), the position of baffle (3 ≤ X 2 ≤ 7), the length of baffle (0 ≤ h ≤ 1.5) and the geometry parameter (2 ≤ X 1 ≤ 4) on flow pattern and heat transfer characteristics are provided a deep insight. The results indicate that the average Nusselt number is an increasing function of Re and φ. The baffle has a significant effect on the flow pattern and heat transfer characteristics. When the length of the baffle increases, the recirculation region behind the backward-facing step shrinks. The average Nusselt number increases by increasing the length of the baffle or moving the baffle towards the backward-facing step.

The present study focuses on the analysis of the fluid dynamics associated with the flapping motion of finite-thickness wings. A two-dimensional numerical model for one and two-winged "clap and fling" stroke has been developed to probe the aerodynamics of insect flight. The influence of kinematic parameters such as the percentage overlap between translational and rotational phase ξ , the separation between two wings δ and Reynolds numbers Re on the evolvement of lift and drag has been investigated. In addition, the roles of the leading and trailing edge vortices on lift and drag in clap and fling type kinematics are highlighted. Based on a surrogate analysis, the overlap ratio ξ is identified as the most influential parameter in enhancing lift. On the other hand, with increase in separation δ, the reduction in drag is far more dominant than the decrease in lift. With an increase in Re (which ranges between 8 and 128), the mean drag coefficient decreases monotonously, whereas the mean lift coefficient decreases to a minimum and increases thereafter. This behavior of lift generation at higher Re was characterized by the "wing-wake interaction" mechanism which was absent at low Re.

The aim of the present study is to characterize the flow patterns, propulsion efficiency and power requirements associated with a self-propelled-heaving thin flat plate in a quiescent medium. In this regard, a numerical model using a shifting discontinuous-grid and based upon multi-relaxation-time lattice Boltzmann method is developed to probe the resulting aerodynamics. The influence of kinematic parameters namely flapping Reynolds number Re f (20 À 100) and plunging amplitude β (0.2-1), and the density ratio ρ* (10 1 À 10 2) on forward flight is pursued. Depending on the kinematics, various periodic vortex shedding characteristics of the plunging plate are observed that lead to modification of the angle of attack as a result of wing-wake interaction and downward jet. The presence of strong vortex dipole at the trailing edge with an attached leading edge vortex are factors responsible for maximum thrust generation. A wing-wake interaction which occurs at low β and high Re f due to weak vortex dissipation and presence of vortex dipole at the trailing edge acting in tandem can lead to achieving high propulsion efficiency. Through surrogate modelling, a set of Pareto-optimal solutions that describe the tradeoff between efficiency and input power for forward flight is presented and offers insight into the design and development of next generation flapping wing micro-air vehicles.