Lattice Boltzmann method for fluid dynamics

In this study, flow past square cylinder has been studied with LBM incorporated with Smagorinsky subgrid scale model at wide range of Reynolds number (102-3.82x105). Numerous results from conventional methods like FD and FVM are compared with present study on corresponding condition with in good agreement which imply that our LBM code works properly and has reasonable accuracy. To be stable simulation over long simulation time, control parameters such as input velocity and fluid viscosity or relaxation time should be chosen in a certain combination. In case of channel flow with square obstacle, decrease of input velocity was good combination with increase of relaxation parameter. Our code to simulate flow past bluff bodies can carry out up to Re of 5x105 with some oscillation on vicinity of obstacle edge. In large scale problem with ExLBM would have computational cost which can be managed by exploit of parallel computation. It should be noted that results in paper are shown in dimensionless form.
Standard LBM has not only limited to apply as shown above turbulent flow, but also restricted to non homogenies and multicomponent flows which are challenged and branched to different type LBM models such as Two Fluid and Phase function model etc. Our future work related to both restrictions. With LBM method we have been striving to solve crucial hydraulics problem such as density current in estuary, sediment transport or bed evaluation and ice formation process in continental rivers.

Geophysical hazards usually involve multiphase flow of dense granular solids and water. Understanding the mechanics of granular flow is of particular importance in predicting the run-out behaviour of debris flows. The dynamics of a homogeneous granular flow involve three distinct scales: the microscopic scale, the meso-scale, and the macroscopic scale.

Conventionally, granular flows are modelled as a continuum because they exhibit many collective phenomena. ecent studies, however, suggest that a continuum law may be unable to capture
the effect of inhomogeneities at the grain scale level, such as orientation of force chains, which are micro-structural effects. Discrete element methods (DEM) are capable of simulating these micro-structural effects, however they are computationally expensive. In the present study, a multi-scale approach is adopted, using both DEM and continuum techniques, to better understand the rheology of granular flows and the limitations of continuum models.

The collapse of a granular column on a horizontal surface is a simple case of granular flow; however, a proper model that describes the flow dynamics is still lacking. In the present study, the generalised interpolation material point method
(GIMPM), a hybrid Eulerian -- Lagrangian approach, is implemented with the Mohr-Coloumb failure criterion to describe the continuum behaviour of granular flows. The granular column collapse is also simulated using DEM to understand the micro-mechanics of the flow.

The limitations of MPM in modelling the flow dynamics are
studied by inspecting the energy dissipation mechanisms. The lack of collisional dissipation in the Mohr-Coloumb model results in longer run-out distances for granular flows in dilute regimes (where the mean pressure is low). However, the model is able to capture the rheology of dense granular flows, such as the run-out evolution of slopes subjected to lateral excitation, where the inertial number I < 0.1.

The initiation and propagation of submarine flows depend mainly on the slope, density, and quantity of the material destabilised. Certain macroscopic models are able to capture simple mechanical behaviours, however the complex physical mechanisms that occur at the grain scale, such as hydrodynamic
instabilities and formation of clusters, have largely been ignored. In order to describe the mechanism of submarine granular flows, it is important to consider both the dynamics of the solid phase and the role of the ambient fluid. In the present study, a two-dimensional coupled Lattice Boltzmann LBM -- DEM technique is developed to understand the micro-scale
rheology of granular flows in fluid. Parametric analyses are performed to assess the influence of initial configuration, permeability, and slope of the inclined plane on the flow. The effect of hydrodynamic forces on the run-out evolution is analysed by comparing the energy dissipation and flow
evolution between dry and immersed conditions.

Lattice Boltzmann method ability is improved to simulate the mixed convection of Water / FMWCNT nanofluid inside a two dimensional microchannel. The influences of gravity on hydrodynamic and thermal domains are studied while the microchannel walls are imposed by a constant thermal heat flux at three different case studies as no-gravity, Ri = 1 and Ri = 10. The flow Reynolds number is chosen as one and the liquid micro flow conditions are involved by B = 0.005, B = 0.01 and B = 0.02. The mass fraction of carbon nanotubes in water are selected as φ = 0, φ = 0.1% and φ = 0.2%. Double population distribution functions of ''f'' and ''g'' are used in lattice Boltzmann method. To the best of author's knowledge, there is no article concerned the way of heat flux boundary condition simulation by LBM considering the buoyancy forces effects on nanofluid slip velocity. Generate a rotational cell due to gravity in entrance region which leads to observe the negative slip velocity phenomenon can be presented as the several interesting achievements of this work.

The claim that we directly apprehend change and succession in our ordinary experience is phenomenologically plausible – after all, we certainly seem to, at least over short intervals. However, there are those who hold that any attempt to grant consciousness temporal breadth falls into incoherence. I argue here that this is wrong, and defend the "extensional" conception of temporal experience over its "retentional" rival. I then argue that this means that reality itself must be dynamic, simply because experience is dynamic, and experience is part of reality. The precise extent to which the dynamism we find in our experience impacts on the rest of the universe depends on the (much contested) relationship between consciousness and the rest of the universe; on some views it will be trivial, on others immense. Of the different metaphysical accounts of the nature of time currently on offer, Presentism is (arguably) the most dynamic. However, Presentism – at least in its standard guise – looks to be irreconcilable with the extensional account of temporal experience. The way forward, I suggest, is to adopt a modified form of Presentism. I conclude by examining the implications of this view of experience for the claim that we might very probably be short-lived "Boltzmann Brains".

Uncertainty quantification was conducted using non – intrusive form of Generalised Polynomial Chaos methods for square inline tube bundles. The input was treated as uncertain. Uncertainties were considered in Reynolds number of the flow and distance between two tubes of square inline tube bundles, P/D. The range were considered as 250 ≤ Re ≤ 1000 and 1.5 ≤ P/D ≤ 5. The desired gPC output was to determine the lift, drag and skin friction coefficient for the input range. At first the gPC method were validated for a univariate and a multi – variate case, cosine function and spring body problem respectively.

• Develop LBM performance to simulate the heat flux of heat source. • Natural convection and mixed convection of inclined driven cavity by LBM. • Modify collision operator and macroscopic velocities equations in LBM. a b s t r a c t Nano scale method of lattice Boltzmann is developed to predict the fluid flow and heat transfer of air through the inclined lid driven 2-D cavity while a large heat source is considered inside it. Two case studies are supposed: first one is a pure natural convection at Grashof number from 400 to 4000 000 and second one is a mixed convection at Richardson number from 0.1 to 10 at various cavity inclination angles. Using LBM to simulate the constant heat flux boundary condition along the obstacle, is presented for the first time while the buoyancy forces affect the velocity components at each inclination angle; hence the collision operator of LBM and also a way to estimate the macroscopic velocities should be modified. Results are shown in the terms of streamlines and isotherms, beside the profiles of velocity, temperature and Nusselt number. It is observed that the present model of LBM is appropriately able to simulate the supposed domain. Moreover, the effects of inclination angle are more important at higher values of Richardson number.

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method [D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262–5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier–Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor–Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

In this paper, the lattice Boltzmann equation (LBE) method is applied for simulation of lid-driven flow in a two-dimensional, rectangular, deep cavity. First, the code is validated for the standard square cavity, and then the results of a deep cavity are presented. Steady results are presented for deep cavities with aspect ratios of 1.5–4, and Reynolds numbers of 50–3200. Several features of the flow, such as the location and strength of the primary vortex, and the corner-eddy dynamics are investigated and compared with previous findings from experiments and theory. Steady results for deep cavities show the existence of corner eddies at the bottom, which coalesce to form a second primary-eddy as the cavity aspect-ratio is increased above a critical value. However, at relatively high Reynolds numbers, the second primary-eddy is formed via a rapid transition of an unsteady wall-eddy. The predicted results from LBE simulations are shown to be consistent with experiments and theory.

In this paper, a three-dimensional lattice Boltzmann model is proposed to simulate pool-boiling phenomena at high-density ratios. The present model is able to predict the temperature field inside the bubble. The three-dimensional multiphase model is validated against the analytical solution of evaporation d 2 law problem and Laplace's law. In addition, effects of different parameters including, Jacob number, gravitational acceleration (g) and surface tension (σ) on bubble departure diameter are presented for further validation. The bubble departure diameter is found to be proportional to g −0.354 and σ 0.5 , and has a linear relation with Jacob number. These results are more consistent with previous experimental correlations when compared with available lattice Boltzmann literature. Furthermore, the dynamic behavior of multiple bubble formation sites such as micro convection and vortex ring mechanism are presented to show the capability of presented model for capturing more complex physical phenomena. To sum up, the proposed three-dimensional lattice Boltzmann model is feasible and accurate for numerical simulations of pool boiling.

Applicability of two kinds of computational-fluid-dynamics method adopting Cahn-Hilliard (CH) and Allen-Cahn (AC)-type diffuse-interface advection equations based on a phase-field model (PFM) is examined to simulation of motions of microscopic incompressible two-phase fluid on solid surface. A capillarity-driven gas-liquid motion in rectangular channel is simulated by use of a PFM method for solving Navier-Stokes (NS) equations and a CH equation, whereas an immiscible liquid-liquid flow in a microchannel with T-junction and square cross section is simulated by use of another PFM method proposed in this study, which adopts a lattice-Boltzmann method based on fictitious particles kinematics as numerical scheme for solving NS equations and an AC equation that is modified to improve volume-of-fluid conservation. The major findings are as follows: (1) effect of capillary force on the dynamic two-phase fluid system with a high density ratio is well predicted for cross-sectional aspect ratio of the channel = 1 and 2; (2) mono-dispersed slug flow pattern transition is reproduced in good agreement with experimental observations in terms of variation in length and interval of droplets as increasing their volumetric flow rates at a constant flow rate ratio = 1. These results prove that the PFM methods can be used for analyzing two-phase fluid motions in various microfluidic devices and micro fabrication processes.

The paper is in French but there are all equations and  an abstract in English.

Fluid Structure Interactions occur in many elds where we study physical phenomena with
an interaction between a solid and a uid. The lattice-Boltzmann method (LBM) is commonly
used in uid mechanics so for the Fluid Structure Interaction problems it is often coupled with
another solver : the LBM solves the uid and the other solver treats the solid. In this thesis the
goal is to solve by the LBM, both the uid and the solid when the latter undergoes transformations
(possibly large) by the uid. Considering it is very common to use LBM to treat the uid
and the latter is often solved by Eulerian's point of view, it makes sense to want to solve the solid
with Eulerian's point of view although it is often solved by Lagrangian's point of view. Besides,
by solving the totality by the LBM we can have an unique solver for the uid and the solid so
we obtain on the one hand a better calculation time and on the other hand we avoid connection
problems between the uid and the solid solvers. Finally, the LBM is easily parallelisable so if
everything (solid and uid) is solved by LBM so we have better calculation times. In view of
all this, there is a clear rationnal for solving FSI problems in large transformations by the LBM.
First, we will present the state of the art on the LBM for uid mechanics or for FSI problems.
Secondly we will treat cases of small perturbations with an adapted formulation. It should be
noted solids are incompressible. We tested three cases found in the literature. After that, we
used another formulation so we were able to solve FSI problems with large transformations
with the LBM. Like small perturbations, solids are incompressible. We tested on three cases
previously mentioned to ensure that the small perturbations are always correctly treated and
we tested cases with large transformations which were also found in the literature where the
authors obtained a numerical solution using other methods. Besides, the LBM is normally
unstable when there is no diusion term in the equation. We will present a method to avoid
this diculty. The verications are on the three cases of small perturbations and on two cases
where we have analytical solutions. We will show for every case mentioned above that our
results were in good agreement with the results in the literature.

Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle and, depending on the pressure drop between inlet and outlet, vapor formation underneath the corner of the sack-wall is observed. The circumstances of cavitation formation are investigated and it is found that the local bulk pressure and mean stress are insufficient to explain the phenomenon. Results obtained in this study strongly suggest that the viscous stress, interfacial contributions to the local pressure, and the Laplace pressure are relevant to the opening of a vapor cavity. This can be described by a generalization of Joseph's criterion that includes these contributions. A macroscopic investigation measuring mass flow rate behavior and discharge coefficient was also performed. As theoretically predicted, mass flow rate increases linearly with the square root of the pressure drop. However, when cavitation occurs, the mass flow growth rate is reduced and eventually it collapses into a choked flow state. In the cavitating regime, as theoretically predicted and experimentally verified, the discharge coefficient grows with the Nurick cavitation number.

Coupling of lattice Boltzmann (LB) and phase-field (PF) methods is discussed for simulation of a range of multiphase flow problems. The local relaxation and shifting operators make the LB method an attractive candidate for the simulation of the single-phase as well as multiphase flows. For simulating interface dynamics, LB methods require to be coupled with an appropriate scheme representing interfacial dynamics. To this end, we have used a model based on the order parameter, which could be either an index function or a phase-field variable, and coupled it with a LB solver for the simulation of various classes of complex multi-physics and multiphase flows. The LB method is used to compute the flow-field, and, in the case of electrodeposition process modeling, the electro-static potential-field. The application of such a coupled LB-PF is illustrated by the solution of a variety of examples. Finally, fast simulation of such a coupled algorithm is achieved using the state-of-art numerical solution acceleration techniques involving preconditioning and multigrid approaches.

Lattice structure offers the potential to produce desirable macro-scale material properties for a wide variety of engineering applications including blast and impact protection system, thermal insulation, structural aircraft and vehicle components body implants. The work presented here to study the characteristics of quasistatic and dynamic behaviour of lattice structure of different materials. Initially cuboidal lattice structures were investigated to study the stress-strain response, failure behaviour and energy absorbing capacity. Drop hammer test were carried out to understand the behaviour of lattice structures under dynamic behaviour. The results obtained shows quasistatic tests are agreeable with dynamic tests.

Lattice Boltzmann method (LBM) has been receiving enormous attention from researcher to solve fluid related phenomena. LBM in fluid dynamics simulation, one meet some difficulties, for instance it becomes unstable for high Reynolds number flows and requires computational time and memory for large scale simulations. To avoid this, we used here the Entropic LBM (ELBM) of Karlin's group [7] and implemented parallel code on graphical processing units (GPU). For parallel computation, we used GPGPU system of Nagaoka University of technology, which is equipped with Tesla M2050 processors. To verify accuracy and stability, we have solved double periodic shear layer flow in serial computation. The accuracy and stability of simulation by ELBM were superior to the simulation of standard LBM. Simulations of flow past a circular cylinder is carried out by parallel ELBM, where Reynolds number varies up to 140000. Using the GPU in simulation, computation time speeds up until 10 times faster than that of using central processing units (CPU). The results show that the parallel code of ELBM can solve two-dimensional turbulent flow in arbitrary geometry at the higher stability condition without using any other stabilization techniques. 1. Introduction The simulation of traditional computational fluid dynamics deals with Navier-Stokes equation (NSE). Unlike this, lattice Boltzmann method (LBM) solves the discrete Boltzmann kinetic equation in its simplified form, known as Bhatnagar-Gross-Krook (BGK) equation. Founded in the eighties of last century, LBM become recently a widely used method of computational fluid dynamics (CFD). In LBM, the fluid is simulated by molecular velocity distribution functions with discrete velocities on regular lattice. There are two operations on the distribution functions: streaming and collision. The fluid molecules propagation is described by streaming, which is non-local operation against the local collision operator, describing the collision between molecules [1]. LBM has its intrinsic feature: easy to parallelize on computer [2]. On the other hand, one of long standing problem in fluid flow simulation is the simulation of turbulent flow at high Reynolds number. In CFD, the turbulent flow simulations are usually performed either by computationally expensive direct numerical simulation of NSE or by solving averaged NSE [3, 4, 5, 6]. Direct application of the LBM for the turbulent flow simulation leads to instability of computation, because of the low viscosity of fluid. Laminar flows at low Reynolds number (Re) become turbulent when Re reached the value of Re=300 in the case of flow past a bluff body. One of the promising method of stabilizing the LBM turbulent computation is the entropic LBM (ELBM) of Karlin's group, in which, the distribution functions are straightened to satisfy the maximum condition of the entropy at the every time step of simulation. In this paper, first we confirm accuracy and performance of the ELBM solving double periodic shear layer flow. Then we perform the calculations of high Reynolds number turbulent flow past a circular cylinder using the ELBM of Karlin et al [7, 8] in parallel algorithm.

For interface-tracking simulation of incompressible two-phase fluids with high density ratios, a new numerical method was proposed by combining Navier-Stokes equations with a phase-field model based on a van der Waals-Cahn-Hilliard free-energy theory. The method was applied to several benchmark problems. Major findings are as follows: (1) The volume flux derived from a local chemical potential gradient in the Cahn-Hilliard equation leads to accurate volume conservation, autonomic reconstruction of gas-liquid interface, and reduction of numerical diffusion and oscillation. (2) The proposed method gave good predictions of pressure increase inside a bubble caused by the surface tension force. (3) A single liquid drop falling in stagnant gas and merging into a stagnant liquid film was successfully simulated.

Artificial dissipation is a well known tool for the improvement of stability of numerical algorithms. However, the use of this technique affects the accuracy of the computation. We analyze various approaches proposed for enhancement of the Lattice Boltzmann Methods (LBM) stability. In addition to some previously known methods, the Multiple Relaxation Time (MRT) models, the entropic lattice Boltzmann method (ELBM), and filtering (including entropic median filtering), we develop and analyze new filtering techniques with independent filtering of different modes. All these methods affect dissipation in the system and may adversely affect the reproduction of the proper physics. To analyze the effect of dissipation on accuracy and to prepare practical recommendations, we test the enhanced LBM methods on the standard benchmark, the 2D lid driven cavity on a coarse grid (101××101 nodes). The accuracy was estimated by the position of the first Hopf bifurcation points in these systems. We find that two techniques, MRT and median filtering, succeed in yielding a reasonable value of the Reynolds number for the first bifurcation point. The newly created limiters, which filter the modes independently, also pick a reasonable value of the Reynolds number for the first bifurcation.

• The stability problem arises for lattice Boltzmann methods in modelling of highly non-equilibrium fluxes.

• Dissipation control is an efficient tool to improve stability but it affects accuracy.

• We analyse the stability–accuracy problem for lattice Boltzmann methods with additional dissipation.

• We compare various methods for dissipation control: Entropic filtering, Multirelaxation methods and Entropic collisions.

• For numerical test we use the lid driven cavity; the accuracy was estimated by the position of the first Hopf bifurcation.

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 wt-%Cu–1 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.

A B S T R A C T Particle collisions play a critical role in determining the fluid-particle interaction. Thus, particulate matters and their interaction within a flow need an accurate treatment through felicitous composite methods. Accordingly, we present a numerical simulation based on a combined Lattice Boltzmann Method (LBM), Immersed Boundary Method (IBM), and Hard Sphere Molecular Dynamics (HSMD) scheme, with applications. This simulation method aims to understand spherical point-particle sedimentation in an incompress-ible Newtonian fluid. A Stokes' drag model implements the hydrodynamic interaction using Ladd's LBM scheme and a momentum exchange based IBM. The HSMD evaluates the discrete particles' kinematics and trajectory. We simulate a 3D single particle settling case as a benchmark. The simulation result exhibits a close match between the terminal particle velocity and an analytical result; it reproduces the expected exponential behavior. Finally, a sedimentation case involving 7200 particles demonstrates the composite schemes' capability to solve the complex interactions. This article discusses the interesting observations and results.

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier–Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Underwater avalanches are a major risk to offshore structures. The mechanisms involved in the initiation and propagation of underwater granular avalanches are complex. They depend mainly on the slope, density, and quantity of material destabilised. Characterising the risk induced by such catastrophic flows requires the development of reliable models. Most models of submarine landslides assume a single homogeneous phase representing the grain-fluid mixture governed by a non-Newtonian fluid behaviour. Although successful in accounting for general phenomenology in a small computation time, such models, defined at a large scale, are limited in describing all features of seabed granular flows. Hence, it is important to understand the mechanism of underwater granular flows at the particle scale. A pending research issue is the parameterization of interactions between the water phase and the sediment phase. Owing to the number of flow variables involved and measurement imprecision, estimating such parameters from laboratory experiments remains difficult. In the present study, sub-particle scale numerical simulations are performed to understand the local phenomena of underwater granular flows. The Discrete Element Method (DEM) is coupled with the Lattice Boltzmann Method (LBM), for fluid-particle interactions, to study the collapse of granular columns in fluids. The coupling of DEM and LBM enables the introduction of water phase and calculation of hydrodynamic forces on grains. D2Q9 Model in LBM is used to simulate the fluid phase. A parameteric analysis is performed to assess the influence of the grain sample characteristics (initial configuration) and the fluid properties (e.g., viscosity) on the evolution of flow and run-out distances. The effect of hydrodynamic forces on the run-out evolution is analysed by comparing the mechanism of energy dissipation and flow evolution in dry and immersed granular flows.

The motion of fluids which are incompressible could be described by the Navier-Stokes differential equations. However, the
three-dimensional Navier-Stokes equations for modelling turbulence misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would greatly affect the field of fluid mechanics. In this paper, which had been published in an international journal in 2010, a reasoned, practical approach towards resolving the issue is adopted and a practical, statistical kind of mathematical solution is proposed.

We describe how regularization of lattice Boltzmann methods can be achieved by modifying dissipation. Classes of techniques used to try to improve regularization of LBMs include flux limiters, enforcing the exact correct production of entropy and manipulating non-hydrodynamic modes of the system in relaxation. Each of these techniques corresponds to an additional modification of dissipation compared with the standard LBGK model. Using some standard 1D and 2D benchmarks including the shock tube and lid driven cavity, we explore the effectiveness of these classes of methods.

In turbulence models we create mathematical models that describe the flow properties of a flowing fluid. A turbulence model is a computational procedure to close the system of mean flow equations and so that a more or less wide variety of flow problems can be calculated. However, far less precision has been achieved in creating a mathematical model that approximates the physical behavior of turbulent flows. Reynolds stress model is used to get the flow behavior and compared with the theoretical solution and the inferences are drawn. I. INTRODUCTION Due to the development in the Computer Aided Design / Computer Aided Engineering technology, now it is possible to analysis the fluid flow problem, in general any engineering problems. The CFD approach has come in this way, when compared to the theoretical and wind tunnel approach. In the present work of flow analysis over cylinder is made for turbulence models and postprocessor velocity contour. Initially the geometry is created and then the fluid domain is discritized by mesh. In the solver and postprocessor its solutions and result are obtained. Basically a theory of CFD-turbulence models and new software tool are applied. This technique may be used for designing of any fluid equipment by using the advantage of CAE. Because of the chaotic-like and apparently random behavior of turbulence, we will need statistical techniques for most of our study of turbulence. CFD is a tool that helps solve a wide range of problems in Fluid Dynamics and Heat transfer. These phenomena are governed by sets of partial differential equations which in most cases have no analytical solution. In addition to the governing equations, we also need the boundary and initial conditions, material properties, and geometrical details in order to completely describe the problem.

Шинжлэх ухааны ихэнхи салбар тэр дундаа инженерчлэлийн салбарын судалгааны чухал чиглэл бол тооцон бодох ухаан юм. Ус, шингэнтэй холбогдсон инженерчлэлийн салбарт уг ухаан нь тооцон бодох шингэний динамик хэмээн нэрлэгдэж салбарын чухал асуудлуудыг шийдэхэд үнэтэй хувь нэмрээ оруулж байна. Энэхүү илтгэлд харьцангуй шинэвтэр шингэний хөдөлгөөнийг тооцон бодох арга болох Латтис Больцманы аргыг (цаашид ЛБА гэх) сүвэрхэг орчин дундуурх шингэний урсгалд хэрхэн ашиглаж байгаа тухай дурьдах юм.  ЛБА нь бусад уламжлалт тооцон бодох аргуудтай (төгсгөлөг аргууд) харьцуулбал сүвэрхэг орчныг загварчлахад маш тохиромжтойн дээр, хэд хэдэн ялгаатай замаар тооцон бодох боломжийг бүрдүүлж өгч байгаа нь хэмжээсийн янз бүрийн түвшинд газрын доорхи усны хөдөлгөөн, түүнд ууссан бодисын тархалт/дисперси зэргийг загварчлах боломжтойг харуулж байна. Энэ илтгэлийн үр дүнд гарсан тооцооны тохирол болон өмнөх ижил төстэй судалгааны материалуудаас үзэхэд ЛБА нь сүвэрхэг орчин дотуурх урсгалын динамик шинж чанарыг загварчлах өндөр бүтээмжтэй, нарийвчлалтай арга гэдгийг баталж байна.

In this paper, we present numerical procedure for liquid-solid phase change of water with Lattice Boltzmann method (LBM). The numerical procedure is composed as follows. Two distribution functions approach will be used to account flow field and temperature field on fixed grids with 9 directional lattices. The enthalpy-based non iterative method is used for phase change of fluid depending on local enthalpy updates. For open channel fluid flow, free surface formulation of single
phase LBM is employed.

A lattice-Boltzmann model (LBM) of unstable flows amid easily permeable obstructions consisting of regular arrays of wires is presented. The obstacles are modeled by forces incorporated as source terms in the LBM equation, following the same procedure as the immersed boundary method. Yet the present method differs from the latter in that the structure is represented by a volumetric array of fixed points. Also each structural point exerts reactive forces governed by the Darcy law, rather than by elastic kinematics. The model is validated against two experiments consisting of air flowing in a channel partially obstructed by arrays of wires, finding excellent agreement. The simulations reveal the formation of complex vortical structures amid the wired region, which can be of interest in understanding natural phenomena or practical applications.

In this paper, a coupled phase-field (PF) and lattice Boltzmann method (LBM) is presented to model the multiphysics phenomenon involving electro-chemical deposition. The deposition (or dissolution) of the electrode is represented using variations of an order-parameter. The time-evolution of an order-parameter is proportional to the variation of a Ginzburg–Landau free-energy functional. Further, the free-energy densities of the two phases are defined based on a dilute or an ideal solution approximation. An efficient LBM is used to obtain the converged electro-static potential field for each physical time-step of the evolution of the PF variable. The coupled approach demonstrates the applicability of the LBM in a multiphysics scenario. The numerical validation for the coupled approach is performed by the simulation of the electrodeposition process of Cu from CuSO4 solution.

Tsunami waves are generated by sea bottom failures, landslides and faults. The concurrent generation of hydro-acoustic waves (HAW), which travel much faster than the tsunami, has received much attention, motivated by their possible exploitation as precursors of tsunamis. This feature makes the detection of HAW particularly well-suited for building an early-warning system. Accuracy and efficiency of the modelling approaches for HAW thus play a pivotal role in the design of such systems. Here, we present a Lattice Boltzmann Method (LBM) for the generation and propagation of HAW resulting from tsunamigenic ground motions and verify it against commonly employed modelling solutions. LBM is well known for providing fast and accurate solutions to both hydrodynamics and acoustics problems, thus it naturally becomes a candidate as a comprehensive computational tool for modelling generation and propagation of HAW.
Keywords: tsunami, hydro-acoustics, Lattice Boltzmann, early warning

A new framework of simulation of reactive flows is proposed based on a coupling between accurate reduced reaction mechanism and the lattice Boltz-mann representation of the flow phenomena. The model reduction is developed in the setting of slow invariant manifold construction, and the simplest lattice Boltzmann equation is used in order to work out the procedure of coupling of the reduced model with the flow solver. Practical details of constructing slow invariant manifolds of a reaction system under various thermodynamic conditions are reported. The proposed method is validated with the two-dimensional simulation of a premixed counterflow flame in the hydrogen-air mixture.

In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known P(n) and S(n) methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.