Lattice Boltzmann Method Code Research Articles

Topology optimization using the lattice Boltzmann method for unsteady natural convection problems

This paper proposes a density-based topology optimization method for natural convection problems using the lattice Boltzmann method (LBM). As the LBM can be developed as a completely explicit scheme, its attractive features over the traditional ones, such as the finite element method, are (1) suitability for solving unsteady flow problems and (2) scalability for large-scale parallel computing. We develop an LBM code for solving unsteady natural convection problems and provide its sensitivity analysis based on the so-called adjoint lattice Boltzmann method. Notably, the adjoint equation is derived from the discrete particle velocity Boltzmann equation and can be solved similarly to the original LBM concerning unsteady natural convection problems. We first show that the proposed method can produce similar results to the previous work in a steady-state natural convection problem. We then demonstrate the efficacy of the proposed method through 2D numerical examples concerning unsteady natural convection. As a large-scale problem, we tackle a 3D unsteady natural convection problem on a parallel supercomputer. All the developed codes written in C++ are available at https://github.com/PANFACTORY/PANSLBM2.git.

Simulation of fluid flow in a lid-driven cavity with different wave lengths corrugated walls using Lattice Boltzmann method

BackgroundThe Lid-driven cavity (LDC) flow is an interesting problem in fluid mechanics. The lattice Boltzmann Method (LBM) is used to simulate fluid flow in a LDC with different wave lengths corrugated walls. MethodsThe D2Q9 model is used for the 2D bounded domain where the analysis of bottom-bounded wall corrugations on the flow features is analyzed. For validation, a square corrugation along the bottom wall with a driven top wall is considered. A lattice size independence study is performed and the LBM code is substantiated with published results for different values of Reynolds number. The code is then modified by using sinusoidal corrugated walls with different wavelengths along the bottom surface. Significant findingThe streamline patterns, vorticity contours and kinetic energy contours are studied for different Reynolds number. Results shown that the position, number and size of vortices depend on the number of corrugations and value of Reynolds number used. The secondary vortices tend to increase in size as the Reynolds number increase. The kinetic energy contours show maximum energy near the top wall which reduces inside the cavity.

Research on thermal performance and optimization design of phase change pin fin heat sink based on Lattice Boltzmann method

This paper reports a numerical research of the phase change materials (PCMs) based pin fin heat sinks for thermal management of battery and electronic device. The 58 semi-refined paraffin and several paraffin/CNTs composites (CNT mass fraction of 5 %, 8 %, 10 %) were adopted as PCMs filled in the heat sink. Lattice Boltzmann method (LBM) was used to numerically study the influence of fin geometry (square fin, circular fin, cross fin), fin number (one to five), fin arrangement (array arrangement, cross arrangement) and PCMs on the working performance (charging time and heat dissipation power) of the heat sinks. The LBM code was solved in Visual Basic. The results report that the four/five square fins (arrangement A) heat sink with 10 % CNT compound paraffin has the shortest charging time and the heat sink with four square fins (arrangement A) and 8 % CNT compound paraffin has the largest heat dissipation power. It is worth noted that compared with square fin heat sinks, the cross fin heat sinks still present 83 % of the heat dissipation power with only 36 % of the fin volume. Besides, aiming at acquiring the largest heat dissipation power, a back propagation neural network-genetic algorithm was developed to optimize the structure of the pin fin heat sink. The corresponding fin number, fin side length and fin distance for the optimized square fin heat sink (arrangement A) are 4, 2.13 mm and 5.88 mm, respectively.

Comparison of a finite volume and two Lattice Boltzmann solvers for swirled confined flows

A finite volume and two Lattice–Boltzmann unsteady, flow solvers using LES (Large Eddy Simulation) were compared in a swirling flow configuration, typical of aeronautical combustion chambers. Numerical results were validated against experimental data collected at EM2C laboratory by comparing pressure losses, mean and RMS velocity profiles on multiple planes and axial velocity spectra. Meshes and the overall numerical setups were individually adjusted for each code to obtain the targeted accuracy before comparing CPU efficiencies.Results confirm that the three LES codes provide high fidelity results, much better than usual RANS especially in terms of RMS data. The analysis of CPU performances shows that LBM (Lattice–Boltzmann Method) solvers are faster than the finite volume solver, even if CPU efficiencies remains of the same order of magnitude. In addition, strong scaling tests from 36 to 900 cores show that the finite volume solver scales more efficiently than the LBM codes, specially when the number of grid points per core is not sufficient.

Computational analysis of naturally oscillating tandem square and circular bluff bodies: a GPU based immersed boundary – lattice Boltzmann approach

ABSTRACT In this study, a fluid-structure interaction solver is employed to explore the flow physics of tandem oscillating square bluff bodies by varying the corner radius. Based on previous research, dynamic behavior, and fluid forces only square and circular bluff bodies are chosen for a supplementary investigation. This study investigates the effects of the streamwise displacement, , of two elastically mounted square and circular bluff bodies in a tandem arrangement. Fluid flows at a Reynolds number of 100 and a fixed mass ratio are used for the upstream and downstream bluff bodies. As the most complex oscillations and wake flows occur adjacent to the approximate natural frequency ratio, thus a constant natural frequency of is defined. To achieve excellent parallel performance, an immersed boundary lattice Boltzmann method code coupled with a structural equation is developed and accelerated using a graphical processing unit. The results for flow-induced vibrations suggest that the flow response characteristics of the tandem oscillating bluff bodies are strong functions of the streamwise displacement. Four different flow regimes of the bluff body arrangements are identified on the basis of response amplitude. Both the square and circular downstream bluff bodies exhibit two peak transverse amplitudes in the existing scrutinized spacing ratios. In addition, the critical spacing ratio values are dissimilar for the two bluff bodies. Moreover, at the end of the spacing ratio (), the wake effects for the downstream square body are amplified, and it oscillates near a single oscillating circular bluff body. Finally, the flow physics, as well as the hydrodynamic force coefficients of the tandem oscillating bluff bodies are also reviewed.

Numerical simulation study of acoustic waves propagation and streaming using MRT-lattice Boltzmann method

This paper presents a numerical investigation of the propagation of acoustic waves generated by a linear acoustic source using the lattice Boltzmann method (LBM). The main objective of this study is to compute the sound pressure and acoustic force produced by a rectangular sound source located at the center of the west wall of a rectangular cavity, filled with water. The sound source is discretized into a set of point sources emitting waves according to the acoustic point source method. The interference between the generated cylindrical waves creates an acoustic beam in the cavity. An analytical study is carried out to validate these numerical results. The error between the numerical and analytical calculations of the wave propagation is also discussed to confirm the validity of the numerical approach. In a second step, the acoustic streaming is calculated by introducing the acoustic force into the LBM code. A characteristic flow structure with two recirculating cells is thus obtained.

A systematic study for determining the optimal relaxation time in the lattice Boltzmann method at low Reynolds numbers

In the lattice Boltzmann method (LBM), the relaxation time plays a significant role in the accuracy of simulation. However, there has been little attention directed toward evaluating the optimal relaxation time in literature. This paper proposes a systematic approach for the determination of the optimal relaxation time, particularly for very-low Reynolds (Re) number flows as analogues for blood flow in micro-vessels. The LBM with D2Q9 lattice model is used to simulate Poiseuille flow in a micro-channel and its accuracy is verified against the analytical solution. It was found that for a given number of grid points in the y-direction, the value of optimal relaxation time predicted analytically differs from that obtained from the numerical solutions. This indicates that the analytical relaxation time should be corrected when used in the LBM code.

Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in multiphase tissue models.

We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation. A membrane boundary condition is presented which is able to accurately represent the effects of thin curvilinear membranes typically found in biological tissues. As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic and mirroring outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate than the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system, as well as on GPUs, is straightforward and efficient. Along with offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a flexible scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous multiphase tissue models and to accommodate sophisticated dMRI sequences.

Transient Response of Longitudinal Fins under Step Changes in Base Temperature and Heat Flux using Lattice Boltzmann Method

The present article reports the transient response of longitudinal fins having linear and non-linear temperature dependent thermal conductivity, convection coefficient and internal heat generation under two cases of base boundary condition, (i) step change in base temperature and (ii) step change in base heat flux. The fin tip is assumed to be adiabatic. Both, linear and non-linear, temperature dependency of thermo-physical properties is addressed in the mathematical formulation and the solution for the above cases is obtained using Lattice Boltzmann method (LBM) implemented in an in-house source code. LBM, being a dynamic method, simulates the macroscopic behavior by using a simple mesoscopic model and offers enormous advantages in terms of simple algorithm to handle even the most typical of boundary conditions that are easy and compact to program even in case of complicated geometries too. Although the transient response of longitudinal fins has been reported earlier, however power law variation of thermo physical properties for the above two base condition has not been reported till date. The present article first establishes the validity of LBM code with existing result and then extends the code for solving the transient response of the longitudinal fin under different sets of application-wise relevant conditions that have not been treated before. Results are reported for several combination of thermal parameter and are depicted in form of graphs.

Simulations for the flow of viscoplastic fluids in a cavity driven by the movement of walls by Lattice Boltzmann Method

The current paper is focused on analyzing the flow of viscoplastic fluid in a cavity that is driven by the two walls. The Lattice Boltzmann method (LBM) is used to solve the discrete Boltzmann equation. To represent the stress-strain rate relationship of viscoplastic fluids, the Bingham Papanastasiou constitutive model is considered. Cavity flow filled with Bingham fluids is considered for validating the present LBM code. After successful validation of the code, the analysis is extended for three dissimilar wall motions-simultaneous and opposed movement of the parallel facing walls, and the simultaneous motion of non-facing walls. The flow dynamics of Bingham fluid is influenced by Reynolds and Bingham numbers which can be studied using velocity and streamline plots. Subsequently, the yielded and un-yielded zones in a cavity have been effectively tracked using the limiting condition of yield stress. Further, the effect of wall motion on the variation of those zones inside a cavity has been studied. Finally, the drag coefficient for considered wall motions is presented.

Graphics process unit accelerated lattice Boltzmann simulation of indoor air flow: Effects of sub-grid scale model in large-eddy simulation

In this present study, three-dimensional lattice Boltzmann method is implemented with the popular turbulence modeling method large-eddy simulation incorporating three different non-dynamic sub-grid scale models Smagorinsky, Vreman, and wall-adapting local eddy-viscosity for finding the inhomogeneous turbulent airflow patterns inside a model room with a partition. The large eddy simulation-lattice Boltzmann method code is validated with the experimental results of Posner’s model, where the model room having one partition at the bottom, one inlet, an outlet placed at top wall considered for the comparisons. The lattice Boltzmann method code is also validated without any sub-grid scale model with the results of lid-driven flow in a cubic cavity. The present numerical simulations are performed by the graphics process unit accelerated parallel programs using compute unified device architecture C platform. Double precession capable a Tesla k40 with 2880 compute unified device architecture cores NVIDIA graphics process unit card has been used for these simulations. Graphics processor units have gained popularity in recent years as a propitious platform for numerical simulation of fluid dynamics. In fact, faster computational task performance in graphics process units is one of the key factors for researchers to choose graphics process unit over conventional central processing units for the implementation of data-intensive numerical methods like lattice Boltzmann method. The effects of the sub-grid scale model have been evaluated in terms of the mean velocity profiles, streamlines as well as turbulence characteristics and found that there are significant differences in the results due to the different sub-grid scale models.

Analysis of the multi-physics approach using the unified lattice Boltzmann framework

This work establishes a unified lattice Boltzmann method (LBM) framework to solve the nuclear reactor multi-physics processes involving the neutron transport and heat transfer processes, wherein all the SN, SP3 and P1 approximations are included for neutron transport simulation. The different physical fields can be solved using the general LBM format with different LBM variables definitions, while the same approach and boundary treatment can be applied due to the unified scheme. No complicated data interpolation is required, and the existing LBM codes can be easily extended. Results show that this unified framework can be used to solve the multi-physics problem in both transient and steady state accurately, and all the SN, SP3 and P1 approximations can be applied. This paper can provide a novel framework for the nuclear reactor multi-physics calculation, and due to the high localization, this framework can further be used to large-scale engineering calculation in parallel.

Pore-Scale Characterization and Simulation of Porous Electrode Material for Vanadium Redox Flow Battery: Effects of Compression on Transport Properties

In this study, X-ray computed tomography (XCT) and pore-scale simulation were employed to investigate the mechanical deformation of a porous electrode material for a vanadium redox flow battery during compression and to quantify its impact on the effective transport properties of the electrode. Pore-scale simulations using the finite element method (FEM), pore-scale modeling (PSM), and lattice Boltzmann method (LBM) were adopted to obtain the deformed geometry and to compute the effective diffusivity, conductivity, and permeability. The structure of a carbon felt was first scanned and reconstructed by XCT; using the results, a 3D model was generated and meshed for solid mechanics simulations. In the FEM simulation, the displacement of the microstructure at different compression ratios (CRs) was investigated considering the contact, friction, extrusion, and bending interactions between the carbon fibers. The relationship between the CR and transport properties was quantified using in-house PSM and LBM codes. The results reveal that the carbon felt is highly anisotropic. When compressed, the displacement of the carbon fibers changes significantly in the through-plane and in-plane directions. The effective diffusivities and permeability of the felt decrease with increasing CR, and its electrical conductivity increases with increasing CR. The present study demonstrates a workflow that combines experimental characterization and solid mechanics simulation to produce deformed solid mechanics models, which can be subsequently employed for mesoscopic simulations in order to obtain effective transport properties. This approach will enable computational investigations into general porous electrode materials, and more importantly, it can be employed to design new materials that can be engineered for optimal performance.

A concise python implementation of the lattice Boltzmann method on HPC for geo-fluid flow

SUMMARY The lattice Boltzmann method (LBM) is a method to simulate fluid dynamics based on modelling distributions of particles moving and colliding on a lattice. The Python scripting language provides a clean programming paradigm to develop codes based on the LBM, however in order to reach performance comparable to compiled languages, it needs to be carefully implemented, maximizing its vectorized tools, mostly integrated in the NumPy module. We present here the details of a Python implementation of a concise LBM code, with the purpose of offering a pedagogical tool for students and professionals in the geosciences who are approaching this technique for the first time. The first half of the paper focuses on how to vectorize a 2-D LBM code and show how if carefully done, this allows performance close to a compiled code. In the second part of the paper, we use the vectorization described earlier to naturally write a parallel implementation using MPI and test both weak and hard scaling up to 1280 cores. One benchmark, Poiseuille flow and two applications, one on sound wave propagation and another on fluid-flow through a simplified model of a rock matrix are finally shown.

Lattice-Boltzmann Simulation and Experimental Validation of a Microfluidic T-Junction for Slug Flow Generation

We investigate the interaction of two immiscible fluids in a head-on device geometry, where both fluids are streaming opposite to each other. The simulations are based on the two-dimensional (2D) lattice Boltzmann method (LBM) using the Rothman and Keller (RK) model. We validate the LBM code with several benchmarks such as the bubble test, static contact angle, and layered flow. For the first time, we simulate a head-on device by forcing periodicity and a volume force to induce the flow. From low to high flow rates, three main flow patterns are observed in the head-on device, which are dripping-squeezing, jetting-shearing, and threading. In the squeezing regime, the flow is steady and the droplets are equal. The jetting-shearing flow is not as stable as dripping-squeezing. Moreover, the formation of droplets is shifted downstream into the main channel. The last flow form is threading, in which the immiscible fluids flow parallel downstream to the outlet. In contrast to other studies, we select larger microfluidic channels with 1-mm channel width to achieve relatively high volumetric fluxes as used in chemical synthesis reactors. Consequently, the capillary number of the flow regimes is smaller than 10−5. In conclusion, the simulation compares well to experimental data.

Numerical simulation of mixed convection heat transfer of fluid in a cavity driven by an oscillating lid using lattice Boltzmann method

Lattice Boltzmann Method (LBM) has been applied for the simulation of a mixed convection heat transfer of two dimensional Newtonian fluid in a square cavity driven by a periodically oscillating lid. The top wall is maintained at higher variable temperature. The developed LBM code in Matlab, is applied for the oscillating lid to simulate the fluid flow and heat transfer in cavity, was validated using various Reynolds and Grashof numbers. Nusselt number was calculated for various pertinent dimensionless groups. Fluid flow and heat transfer characteristics were examined in the domain of Reynolds number, Grashof number, the dimensionless lid oscillation frequency and different values of temperature. Such that: 102⩽Re⩽103, 102⩽Gr⩽106, 0.1⩽ω⩽5, the Prandtl number was fixed as 0.71. The results show that the variation of the Reynolds and Grashof numbers has an effect on energy transport process and drag force behavior depending on the conduct of the velocity cycle. Moreover the variation of Rayleigh number and period of the heated portion has an effect on the transfer rate on convective structures.

A distributed parallel multiple-relaxation-time lattice Boltzmann method on general-purpose graphics processing units for the rapid and scalable computation of absolute permeability from high-resolution 3D micro-CT images

Digital rock physics (DRP) is a rapidly evolving technology targeting fast turnaround times for repeatable core analysis and multi-physics simulation of rock properties. We develop and validate a rapid and scalable distributed-parallel single-phase pore-scale flow simulator for permeability estimation on real 3D pore-scale micro-CT images using a novel variant of the lattice Boltzmann method (LBM). The LBM code implementation is designed to take maximum advantage of distributed computing on multiple general-purpose graphics processing units (GPGPUs). We describe and extensively test the distributed parallel implementation of an innovative LBM algorithm for simulating flow in pore-scale media based on the multiple-relaxation-time (MRT) model that utilizes a precise treatment of body force. While the individual components of the resulting simulator can be separately found in various references, our novel contributions are (1) the integration of all of the mathematical and high-performance computing components together with a highly optimized code implementation and (2) the delivery of quantitative results with the simulator in terms of robustness, accuracy, and computational efficiency for a variety of flow geometries including various types of real rock images. We report on extensive validations of the simulator in terms of accuracy and provide near-ideal distributed parallel scalability results on large pore-scale image volumes that were largely computationally inaccessible prior to our implementation. We validate the accuracy of the MRT-LBM simulator on model geometries with analytical solutions. Permeability estimation results are then provided on large 3D binary microstructures including a sphere pack and rocks from various sandstone and carbonate formations. We quantify the scalability behavior of the distributed parallel implementation of MRT-LBM as a function of model type/size and the number of utilized GPGPUs for a panoply of permeability estimation problems.

Three-dimensional finite amplitude electroconvection in dielectric liquids

Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state to turbulence once the system loses its linear stability. In addition, the numerically predicted linear and finite amplitude stability criteria of different flow patterns are discussed.

Numerical predictions of laminar and turbulent forced convection: Lattice Boltzmann simulations using parallel libraries

This paper presents the performance comparison of various parallel lattice Boltzmann codes for simulation of incompressible laminar convection in 2D and 3D channels. Five different parallel libraries namely; matlabpool, pMatlab, GPU-Matlab, OpenMP and OpenMP+OpenMPI were used to parallelize the serial lattice Boltzmann method code. Domain decomposition method was adopted for parallelism for 2D and 3D uniform lattice grids. Bhatnagar-Gross-Krook approximation with lattice types D2Q9, D2Q19 and D2Q5, D2Q6 were considered to solve 2D and 3D fluid flow and heat transfer respectively. Parallel computations were conducted on a workstation and an IBM HPC cluster with 32 nodes. Laminar forced convection in a 2D and turbulent forced convection in a 3D channels was considered as a test case. The performance of parallel LBM codes was compared with serial LBM code. Results show that for a given problem, parallel simulations using matlabpool and pMatlab library perform almost equal. Parallel simulations using C language with OpenMP libraries were 10 times faster than simulations involving Matlab parallel libraries. Parallel simulations with OpenMP+OpenMPI were 0.35 times faster than the reported parallel lattice Boltzmann method code in the literature.

Modelling urban airflow and natural ventilation using a GPU-based lattice-Boltzmann method

Simulation of urban airflow and ventilation potential is desirable for building design, however the complex and transient nature of flows in urban environments makes this a challenging task. This study aims to evaluate the capability of a lattice-Boltzmann method (LBM) code deployed on a graphical processing unit (GPU) using a large eddy sub-grid turbulence model for cross-flow ventilation of an idealised cubical building at wind-tunnel scale. ANSYS Fluent is used as a numerical comparison. Façade pressure and ventilation of the cube are investigated for parallel and perpendicular wind directions with the building in isolation and regular array format. Pressures, velocities and ventilation rates are compared to experimental data from wind tunnel and full-scale experiments of the Silsoe cube. Simulations compare favourably with experimental values and between each other. When the cube was surrounded by other cubes, simulations suggest that vortex shedding from up-wind buildings provides pulsating ventilation, improving airflow ingress in the parallel wind cases. A parametric study showed that doubling surrounding building height had a small negative effect on ventilation but was mitigated by high levels of downdraft and flow fluctuations in the vertical plane. Comparatively, doubling the central building height had a net positive effect but caused high internal airspeeds for both angles. The LBM code running on one GPU was several orders of magnitude faster than Fluent with similar accuracy. Simulation time using the LBM approach was several orders of magnitude lower than Fluent.