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The present work aims to deal with simulation of turbulent duct flow using generalized lattice Boltzmann equation (GLBE) in which large eddy simulation was employed.

The sub-grid scale turbulence effects were simulated through a shear-improved Smagorinsky model (SISM) which is capable of predicting turbulent near wall region accurately without any wall function. Computations were done for fully developed turbulent square duct flow at Ret=300, based on duct width and average friction velocity.

Results obtained for turbulent duct flow reveal that the GLBE in conjunction with SISM is able to correctly predict the existence of secondary flows and the computed detailed structure of first- and second-order statistics of main and secondary motions. The methodology is validated by comparing with previously published data. It is concluded that such framework is capable of predicting accurate results for turbulent duct flow. In addition, the operations in the present method are local; it can be easily programmed for parallel machines.

The numerical method, including generalized lattice Boltzmann method with forcing term and implementation of SISM in GLBE, is used for the first time to simulate turbulent duct flow.

The lattice Boltzmann simulation of fluid flow in partial porous geometries with curved porous-fluid interfaces has not been investigated yet. It is mainly because of the lack of a method in the lattice Boltzmann framework to model the hydrodynamic compatibility conditions at curved porous-fluid interfaces, which is required for the two-domain approach. Therefore, the purpose of this study is to develop such a method.

This research extends the non-equilibrium extrapolation lattice Boltzmann method for satisfying no-slip conditions at curved solid boundaries, to model hydrodynamic compatibility conditions at curved porous-fluid interfaces.

The proposed method is tested against the results available from conventional numerical methods via the problem of fluid flow through and around a porous circular cylinder in crossflow. As such, streamlines, geometrical characteristics of recirculating wakes and drag coefficient are validated for different Reynolds (5 ≤ Re ≤ 40) and Darcy (10⁻⁵ ≤ Da ≤ 5 × 10⁻¹) numbers. It is also shown that without applying any compatibility conditions at the interface, the predicted flow structure is not satisfactory, even for a very fine mesh. This result highlights the importance of the two-domain approach for lattice Boltzmann simulation of the fluid flow in partial porous geometries with curved porous-fluid interfaces.

No research is found in the literature for applying the hydrodynamic compatibility conditions at curved porous-fluid interfaces in the lattice Boltzmann framework.

The screw extruder is applied in cement-three-dimensional (3D) printing. The cement paste flow in 3D printing is the typical Herschel–Bulkley fluid. To understand the flow in the channel, the improved lattice Boltzmann method (LBM) is proposed.

For Herschel–Bulkley flow, an improved LBM is presented to avoid the poor stability and accuracy. The non-Newtonian effect is regard as a special forcing term. The Poiseuille flow is taken to discuss the detailed process of the method. With the method, the analytical solution and numerical solution are obtained and compared. Then, the effect of the initial yield stress on the numerical solution is both explored by the shear-thickening fluid and the shear-thinning fluid. Moreover, the variations of the relative errors under different lattice nodes and different power-law indexes are analyzed. Finally, the method is applied into the simulation of the flow in the extruder of cement-3D printing.

The results show that the improved method is effective for Herschel–Bulkley fluids, which can simulate the flow in the extruder stably and accurately.

The simulation can contribute to understand the cement paste flow in the screw extruder, which helps to optimize the structure of the extruder in the following periods.

The improve method provide a new way to analyze the flow in the extruder of cement-3D printing. Also, in the past research, LBM for Herschel–Bulkley fluid is ignored, whereas the study can provide the reference for the numerical simulation.

The purpose of this paper is to apply the lattice Boltzmann method (LBM) to simulate mixed flow, which combines natural convection for temperature difference and forced convection for lid driven, in a two‐dimensional rectangular cavity over a wide range of aspect ratios (A), Rayleigh numbers (Ra) and Reynolds numbers (Re).

The LBM is applied to simulate the mixed flow. A multi‐relaxation technique was used successfully. A scale order analysis helped the understanding and predicting the overall heat transfer.

In the considered lid driven cavity, the Richardson number emerges as a measure of relative importance of natural and forced convection modes on the heat transfer. An expression of the overall heat transfer depending on the cavity slender (A) is deduced. The validity of the obtained expression was checked in mixed convection under the condition of low Richardson number (Ri) and the limitation condition was deduced.

This paper has implications for cooling system optimization and LBM technique development.

This paper presents a new cooling configuration, avoiding critical situation where the opposing effect induce weak heat transfer; and a stable and fast LBM approach allowing complex geometry treatment.

The purpose of this paper is to investigate the laminar flow and heat transfer characteristics in a two‐dimensional horizontal channel with two square blocks placed side‐by‐side using a numerical scheme based on a coupling between the lattice Boltzmann method and the finite difference method.

The multiple‐relaxation‐time (MRT) lattice Boltzmann equation model coupled with the finite difference method are used to predict numerically the velocity and the temperature fields.

A complex structure of the fluid flow was observed for various dimensionless block separation distance (G). An unsteady flow was found when the two blocks are placed side by side (G = 0). For G < 1.5, the presence of each block develops the street of Van Karman which generates complex binary vortex street. In the opposite case (G > 1.5), the effect of this parameter (G) on the fluid is reduced, whereas, the distance between the blocks and the nearest walls have a great influence on the fluid flow and the heat transfer. When the obstacles are posed on the walls (G = 3), an important heat exchange between the blocks and the nearest walls is noted.

This study offers more knowledge on natural convection in an obstructed channel. Furthermore, this work shows the effectiveness of the MRT lattice Boltzmann equation model for this kind of geometry.

The purpose of this paper is to model the convective flows in a room equipped by a glass door and a heated floor of length l = 0.8 × H and submitted to a sinusoidal temperature profile and mono alternative temperature profile.

The paper opts for a numerical study of convective flows in a large scale cavity using the Lattice Boltzmann Method (LBM) by considering a two dimensions (2D) square cavity of side H and filled by air (Pr = 0.71). All the vertical walls, the ceiling and the rest of the floor are thermally insulated, the hot portion of length l = 0.8×H is heated with two imposed temperature profiles of amplitude values 0.2 ≤  a  ≤ 0.6 and for two different periods ζ = ζ0 and ζ = 0.4×ζ0. One of the vertical walls has a cold portion θ_c = 0 that represents the glass door.

A systematic study of the flow structure and heat transfer is carried out considering principal control parameters: amplitude “a” and period ζ for Rayleigh number Ra = 10⁸. Effects of these parameters on results are presented in terms of isotherms, streamlines, profiles of velocities, temperature in the cavity, global and local Nusselt number. It has been found that an increase in amplitude or period increases the amplitude of the temperature in the core of cavity. The Nusselt number increases when the amplitude “a” of the imposed temperature increases, but this later is not affected by variation of the period.

The authors used LBM to simulate the convective flows in a cavity at high Ra, heated from below by tow imposed temperature profiles. Indeed, they simulate a local equipped by a solar water heater (SWH). The floor is subjected to a periodic heating: Sinusoidal heating (Case 1) for which the temperature varies sinusoidally (SWH without a supplement), and mono alternation heating (Case 2), the temperature evolves like a redressed signal (SWH with a supplement). The considered method has been successfully validated and compared with the previous work. The study has been conducted using several control parameters such as the signal amplitude and period in the case of turbulent convection. This allowed us to obtain a considerable set of results that can be used for engineering.

Accurately evaluating fluid flow behaviors and determining permeability for deforming porous media is time-consuming and remains challenging. This paper aims to propose a novel machine-learning method for the rapid estimation of permeability of porous media at different deformation stages constrained by hydro-mechanical coupling analysis.

A convolutional neural network (CNN) is proposed in this paper, which is guided by the results of finite element coupling analysis of equilibrium equation for mechanical deformation and Boltzmann equation for fluid dynamics during the hydro-mechanical coupling process [denoted as Finite element lattice Boltzmann model (FELBM) in this paper]. The FELBM ensures the Lattice Boltzmann analysis of coupled fluid flow with an unstructured mesh, which varies with the corresponding nodal displacement resulting from mechanical deformation. It provides reliable label data for permeability estimation at different stages using CNN.

The proposed CNN can rapidly and accurately estimate the permeability of deformable porous media, significantly reducing processing time. The application studies demonstrate high accuracy in predicting the permeability of deformable porous media for both the test and validation sets. The corresponding correlation coefficients (R²) is 0.93 for the validation set, and the R² for the test set A and test set B are 0.93 and 0.94, respectively.

This study proposes an innovative approach with the CNN to rapidly estimate permeability in porous media under dynamic deformations, guided by FELBM coupling analysis. The fast and accurate performance of CNN underscores its promising potential for future applications.

The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid‐driven flow in a three‐dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two‐dimensional (2D) cavity.

The second‐order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25‐4) and Reynolds numbers (0.01‐1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier‐Stokes (NS) equations and with available experimental data.

The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side‐walls in transverse direction (in 3D), due to which the vorticity in the core‐region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry‐plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid‐motion are observed; these are weak at low Reynolds numbers, but become quite strong at high Reynolds numbers.

The findings will be useful in the study of variety of enclosed fluid flows.

This paper attempts to deal with the presentation of a numerical investigation of the laminar‐free convective heat transfer in a square enclosure containing a solid cylinder located at an arbitrary position. Effects of the cylinder position on the heat transfer and the flow structures inside the cavity are to be studied and highlighted.

The numerical code is based on the hybrid scheme with the lattice Boltzmann and the alternating‐directional implicit (ADI) splitting scheme. The energy equation is solved by ADI scheme and the flow field velocities have been computed using the lattice Boltzmann method (LBM). The bounce‐back condition combined with quadratic interpolation is used at solid boundaries.

The predicted results show that the cylinder location has a significant effect on the heat transfer. It is observed that: when the inner body does not generate heat, most of the heat transfer takes place if the body is located at the center of the enclosure. When the cylinder generates heat and is displaced from the left towards the right and from the lower part towards the upper part of the cavity, the heat transfer rate decreases on the hot wall and increases on the cold wall.

The fluid flow (air) is assumed to be incompressible, laminar and 2D. The viscous heat dissipation is neglected in the energy equation and all physical proprieties are constant except for the density, whose variation with temperature is allowed for in the buoyancy term.

Natural convection in heated enclosures, housing inner bodies has received significant attention because of its interest and importance in industrial applications. Some applications are solar collectors, fire research, electronic cooling, aeronautics, chemical apparatus, building constructions, nuclear engineering, etc.

The paper contributes to the development of the LBM. In particular, it was found that the inherent numerical instabilities of this LBE are not modified by coupling with temperature. This is a good improvement compared to what is observed in the simulations of thermal systems using the full LBE formulation where the energy conservation is taken into account.

The purpose of this paper is to present a fast and bare bones implementation of a numerical method for quickly simulating turbulent thermal flows on GPUs. The work also validates earlier research showing that the lattice Boltzmann method (LBM) method is suitable for complex thermal flows.

A dual lattice hydrodynamic (D3Q27) thermal (D3Q7) multiple-relaxation time LBM model capable of thermal DNS calculations is implemented in CUDA.

The model has the same computational performance compared to earlier publications of similar LBM solvers. The solver is validated against three benchmark cases for turbulent thermal flow with available data and is shown to be in excellent agreement.

The combination of a D3Q27 and D3Q7 stencil for a multiple relaxation time -LBM has, to the authors’ knowledge, not been used for simulations of thermal flows. The code is made available in a public repository under a free license.