A LBM–DEM solver for fast discrete particle simulation of particle–fluid flows

The lattice Boltzmann method (LBM) for simulating fluid phases was coupled with the discrete element method (DEM) for studying solid phases to formulate a novel solver for fast discrete particle simulation (DPS) of particle–fluid flows. The fluid hydrodynamics was obtained by solving LBM equations instead of solving the Navier–Stokes equation by the finite volume method (FVM). Interparticle and particle–wall collisions were determined by DEM. The new DPS solver was validated by simulating a three-dimensional gas–solid bubbling fluidized bed. The new solver was found to yield results faster than its FVM–DEM counterpart, with the increase in the domain-averaged gas volume fraction. Additionally, the scalability of the LBM–DEM DPS solver was superior to that of the FVM–DEM DPS solver in parallel computing. Thus, the LBM–DEM DPS solver is highly suitable for use in simulating dilute and large-scale particle–fluid flows.     

Upscaling LBM-TPM simulation approach of Darcy and non-Darcy fluid flow in deformable,heterogeneous porous media

This paper presents a numerical approach for the simulation of fluid flow through porous media by proposing a theoretical and numerical meso-to-macro multiscale framework, which combines the advantages of the lattice Boltzmann method (LBM) with the continuum Theory of Porous Media (TPM) to efficiently and accurately model fluid transport in heterogeneous porous media. In particular, LBM presents an alternative to experiments by studying the flow from a mesoscopic perspective, which in turn, allows the derivation of the material parameters needed for simulating the flow in the macroscopic TPM model. In this work, a meso-macro hierarchic upscaling scheme is applied to investigate the deformation-dependent intrinsic permeability properties and the Darcy/non-Darcy fluid flow regime. Concerning the mesoscale, the intrinsic permeability of the porous domain is computed by means of the LBM model at the first stage. Subsequently, deformation of the medium takes place in furtherance of determining the relation of the aforementioned deformation dependency. Thereupon, these findings are input into the TPM model in order to compute the primary unknown variables, where special focus is laid on the stability challenges in the compaction and near compaction states. With respect to the criteria of non-Darcy fluid flow, the conditions of its onset, i.e. the induced pressure gradient and mean fluid flow velocity, are computed as well using the LBM solver and conveyed afterwards to the macroscopic TPM model. Herein, the non-Darcy intrinsic permeability has been investigated in the TPM approach based on the Forchheimer equation. Simulations done on a synthetic porous micro-structure show that the combined framework proved to stand well between the two approaches.     

Simulation of three‐dimensional flows over moving objects by an improved immersed boundary–lattice Boltzmann method

An improved immersed boundary–lattice Boltzmann method (IB–LBM) developed recently [28] was applied in this work to simulate three‐dimensional (3D) flows over moving objects. By enforcing the non‐slip boundary condition, the method could avoid any flow penetration to the wall. In the developed IB–LBM solver, the flow field is obtained on the non‐uniform mesh by the efficient LBM that is based on the second‐order one‐dimensional interpolation. As a consequence, its coefficients could be computed simply. By simulating flows over a stationary sphere and torus [28] accurately and efficiently, the proposed IB–LBM showed its ability to handle 3D flow problems with curved boundaries. In this paper, we further applied this method to simulate 3D flows around moving boundaries. As a first example, the flow over a rotating sphere was simulated. The obtained results agreed very well with the previous data in the literature. Then, simulation of flow over a rotating torus was conducted. The capability of the improved IB–LBM for solving 3D flows over moving objects with complex geometries was demonstrated via the simulations of fish swimming and dragonfly flight. The numerical results displayed quantitative and qualitative agreement with the date in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Lattice Boltzmann modeling of pore‐scale fluid flow through idealized porous media

In order to capture the hydro‐mechanical impacts on the solid skeleton imposed by the fluid flowing through porous media at the pore‐scale, the flow in the pore space has to be modeled at a resolution finer than the pores, and the no‐slip condition needs to be enforced at the grain–fluid interface. In this paper, the lattice Boltzmann method (LBM), a mesoscopic Navier–Stokes solver, is shown to be an appropriate pore‐scale fluid flow model. The accuracy and lattice sensitivity of LBM as a fluid dynamics solver is demonstrated in the Poiseuille channel flow problem (2‐D) and duct flow problem (3‐D). Well‐studied problems of fluid creeping through idealized 2‐D and 3‐D porous media (J. Fluid Mech. 1959; 5 (2):317–328, J. Fluid Mech. 1982; 115 :13–26, Int. J. Multiphase Flow 1982; 8 (4):343–360, Phys. Fluids A 1989; 1 (1):38–46, Int. J. Numer. Anal. Meth. Geomech. 1999; 23 :881–904, Int. J. Numer. Anal. Meth. Geomech. 2010; DOI: 10.1002/nag.898, Int. J. Multiphase Flow 1982; 8 (3):193–206) are then simulated using LBM to measure the friction coefficient for various pore throats. The simulation results agree well with the data reported in the literature. The lattice sensitivity of the frictional coefficient is also investigated. Copyright © 2010 John Wiley & Sons, Ltd.     

Lattice Boltzmann modeling of shallow water flows over discontinuous beds

Numerical modeling of shallow water flows over discontinuous beds is presented. The flows are described with the shallow water equations and the equations are solved using the lattice Boltzmann method (LBM) with single relaxation time (Bhatnagar–Gross–Krook‐LBM (BGK‐LBM)) and the multiple relaxation time (MRT‐LBM). The weighted centered scheme for force term together with the bed height for a bed slope is described to improve simulation of flows over discontinuous bed. Furthermore, the resistance stress is added to include the local head loss caused by flow over a step. Four test cases, one‐dimensional tidal over regular bed and steps, dam‐break flows, and two‐dimensional shallow water flow over a square block, are considered to verify the present method. Agreements between predictions and analytical solutions are satisfactory. Furthermore, the performance and CPU cost time of BGK‐LBM and MRT‐LBM are compared and studied. The results have shown that the lattice Boltzmann method is simple and accurate for simulating shallow water flows over discontinuous beds. This demonstrates the capability and applicability of the lattice Boltzmann method in modeling shallow water flows on bed topography with a discontinuity in practical hydraulic engineering. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical simulation of laminar jet-forced flow using lattice Boltzmann method

In the paper, a numerical study on symmetrical and asymmetrical laminar jet-forced flows is carried out by using a lattice Boltzmann method （LBM） with a special boundary treatment. The simulation results are in very good agreement with the available numerical prediction. It is shown that the LBM is a competitive method for the laminar jet-forced flow in terms of computational efficiency and stability.     

Unstructured lattice Boltzmann method in three dimensions

Over the last decade, the lattice Boltzmann method (LBM) has evolved into a valuable alternative to continuum computational fluid dynamics (CFD) methods for the numerical simulation of several complex fluid‐dynamic problems. Recent advances in lattice Boltzmann research have considerably extended the capability of LBM to handle complex geometries. Among these, a particularly remarkable option is represented by cell‐vertex finite‐volume formulations which permit LBM to operate on fully unstructured grids. The two‐dimensional implementation of unstructured LBM, based on the use of triangular elements, has shown capability of tolerating significant grid distortions without suffering any appreciable numerical viscosity effects, to second‐order in the mesh size. In this work, we present the first three‐dimensional generalization of the unstructured lattice Boltzmann technique (ULBE as unstructured lattice Boltzmann equation), in which geometrical flexibility is achieved by coarse‐graining the lattice Boltzmann equation in differential form, using tetrahedrical grids. This 3D extension is demonstrated for the case of 3D pipe flow and moderate Reynolds numbers flow past a sphere. The results provide evidence that the ULBE has significant potential for the accurate calculation of flows in complex 3D geometries. Copyright © 2005 John Wiley & Sons, Ltd.     

A new cross-scaling method to deal with the porous flow problem

The finite volume method (FVM) and the lattice Boltzmann method (LBM) are coupled with each other to construct a new cross-scaling method to deal with the porous flow problem. To check the effectiveness of our developed cross-scaling LBM—FVM, the above mentioned problem is also solved by the well known LBM—LBM. Based on the data checking of the published data and the results of LBM—FVM and LBM—LBM, good agreement is observed.     

A hybrid phase field multiple relaxation time lattice Boltzmann method for the incompressible multiphase flow with large density contrast

A hybrid phase field multiple relaxation time lattice Boltzmann method (LBM) is presented in this paper for simulation of multiphase flows with large density contrast. In the present method, the flow field is solved by a lattice Boltzmann equation. Concurrently, the interface of two fluids is captured by solving the macroscopic Cahn‐Hilliard equation using the upwind scheme. To be specific, for simulation of the flow field, an lattice Boltzmann equation (LBE) model developed in Shao et al. (Physical Review E, 89 (2014), 033309) for consideration of density contrast in the momentum equation is used. Moreover, in the present work, the multiple relaxation time collision operator is applied to this LBE to enable simulation of problems with large viscosity contrast or high Reynolds number. For the interface capturing, instead of solving another set of LBE as in many phase field LBMs, the macroscopic Cahn‐Hilliard equation is directly solved by using a weighted essentially non‐oscillatory scheme. In this way, the present hybrid phase field LBM shares full advantages of the phase field LBM while enhancing numerical stability. The ability of the present method to simulate multiphase flow problems with large density contrast is demonstrated by several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

A high‐order compact finite‐difference lattice Boltzmann method for simulation of steady and unsteady incompressible flows

A high‐order compact finite‐difference lattice Boltzmann method (CFDLBM) is proposed and applied to accurately compute steady and unsteady incompressible flows. Herein, the spatial derivatives in the lattice Boltzmann equation are discretized by using the fourth‐order compact FD scheme, and the temporal term is discretized with the fourth‐order Runge–Kutta scheme to provide an accurate and efficient incompressible flow solver. A high‐order spectral‐type low‐pass compact filter is used to stabilize the numerical solution. An iterative initialization procedure is presented and applied to generate consistent initial conditions for the simulation of unsteady flows. A sensitivity study is also conducted to evaluate the effects of grid size, filtering, and procedure of boundary conditions implementation on accuracy and convergence rate of the solution. The accuracy and efficiency of the proposed solution procedure based on the CFDLBM method are also examined by comparison with the classical LBM for different flow conditions. Two test cases considered herein for validating the results of the incompressible steady flows are a two‐dimensional (2‐D) backward‐facing step and a 2‐D cavity at different Reynolds numbers. Results of these steady solutions computed by the CFDLBM are thoroughly compared with those of a compact FD Navier–Stokes flow solver. Three other test cases, namely, a 2‐D Couette flow, the Taylor's vortex problem, and the doubly periodic shear layers, are simulated to investigate the accuracy of the proposed scheme in solving unsteady incompressible flows. Results obtained for these test cases are in good agreement with the analytical solutions and also with the available numerical and experimental results. The study shows that the present solution methodology is robust, efficient, and accurate for solving steady and unsteady incompressible flow problems even at high Reynolds numbers. Copyright © 2014 John Wiley & Sons, Ltd.     

Lattice Boltzmann method for simulating particle–fluid interactions

The lattice Boltzmann method （LBM） has gained increasing popularity in the last two decades as an alternative numerical approach for solving fluid flow problems. One of the most active research areas in the LBM is its application in particle-fluid systems, where the advantage of the LBM in efficiency and parallel scalability has made it superior to many other direct numerical simulation （DNS） techniques. This article intends to provide a brief review of the application of the LBM in particle-fluid systems. The numerical techniques in the LBM pertaining to simulations of particles are discussed, with emphasis on the advanced treatment for boundary conditions on the particle-fluid interface. Other numerical issues, such as the effect of the internal fluid, are also briefly described. Additionally, recent efforts in using the LBM to obtain closures for particle-fluid drag force are also reviewed.     

不同壁面绕流特性的格子Boltzmann模拟研究

为了探讨不同壁面的绕流特性,针对粘性流场中,不同壁面诱导的涡脱落现象以及升阻力系数等流场特性进行了格子Boltzmann数值研究。利用基于分子动理论的格子Boltzmann方法(LBM)求解Navier-Stokes方程,实现对流体运动的描述,针对不同的壁面条件,分别采用不同的格子Boltzmann流-固壁面处理方法。采用Half-way反弹边界条件来处理平直壁面,而曲壁面则采用LBM与有限差分法相结合的形式进行处理,计入了壁面与标准网格不重合对结果造成的影响。开发相应的计算程序,计算结果与已发表文献结果吻合良好,验证了数值模型的正确性。同时,探讨了进出口边界与钝体中心的距离对结果的影响。对比分析了不同壁面的绕流模型中升阻力系数、斯托罗哈数和涡量云图等,并进一步研究了雷诺数条件的影响。结果表明,不同壁面的绕流特性具有明显差异,且同时受雷诺数的显著影响;一般地,平直壁面对于来流作出的响应更迅速。     

Lattice Boltzmann methods for global linear instability analysis

Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier–Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.     

On the immersed boundary‐lattice Boltzmann simulations of incompressible flows with freely moving objects

For simulating freely moving problems, conventional immersed boundary‐lattice Boltzmann methods encounter two major difficulties of an extremely large flow domain and the incompressible limit. To remove these two difficulties, this work proposes an immersed boundary‐lattice Boltzmann flux solver (IB‐LBFS) in the arbitrary Lagragian–Eulerian (ALE) coordinates and establishes a dynamic similarity theory. In the ALE‐based IB‐LBFS, the flow filed is obtained by using the LBFS on a moving Cartesian mesh, and the no‐slip boundary condition is implemented by using the boundary condition‐enforced immersed boundary method. The velocity of the Cartesian mesh is set the same as the translational velocity of the freely moving object so that there is no relative motion between the plate center and the mesh. This enables the ALE‐based IB‐LBFS to study flows with a freely moving object in a large open flow domain. By normalizing the governing equations for the flow domain and the motion of rigid body, six non‐dimensional parameters are derived and maintained to be the same in both physical systems and the lattice Boltzmann framework. This similarity algorithm enables the lattice Boltzmann equation‐based solver to study a general freely moving problem within the incompressible limit. The proposed solver and dynamic similarity theory have been successfully validated by simulating the flow around an in‐line oscillating cylinder, single particle sedimentation, and flows with a freely falling plate. The obtained results agree well with both numerical and experimental data. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulating 3D deformable particle suspensions using lattice Boltzmann method with discrete external boundary force

A method for direct numerical analysis of three‐dimensional deformable particles suspended in fluid is presented. The flow is computed on a fixed regular ‘lattice’ using the lattice Boltzmann method (LBM), where each solid particle is mapped onto a Lagrangian frame moving continuously through the domain. Instead of the bounce‐back method, an external boundary force (EBF) is used to impose the no‐slip boundary condition at the fluid–solid interface for stationary or moving boundaries. The EBF is added directly to the lattice Boltzmann equation. The motion and orientation of the particles are obtained from Newtonian dynamics equations. The advantage of this approach is outlined in comparison with the standard and higher‐order interpolated bounce‐back methods as well as the LBM immersed‐boundary and the volume‐of‐fluid methods. Although the EBF method is general, in this application, it is used in conjunction with the lattice–spring model for deformable particles. The methodology is validated by comparing with experimental and theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

COMPARISON OF ACCURACY AND PERFORMANCE FOR LATTICE BOLTZMANN AND FINITE DIFFERENCE SIMULATIONS OF STEADY VISCOUS FLOW

The lattice Boltzmann method (LBM) is used to simulate flow in an infinite periodic array of octagonal cylinders. Results are compared with those obtained by a finite difference (FD) simulation solved in terms of streamfunction and vorticity using an alternating direction implicit scheme. Computed velocity profiles are compared along lines common to both the lattice Boltzmann and finite difference grids. Along all such slices, both streamwise and transverse velocity predictions agree to within 0ċ5% of the average streamwise velocity. The local shear on the surface of the cylinders also compares well, with the only deviations occurring in the vicinity of the corners of the cylinders, where the slope of the shear is discontinuous. When a constant dimensionless relaxation time is maintained, LBM exhibits the same convergence behaviour as the FD algorithm, with the time step increasing as the square of the grid size. By adjusting the relaxation time such that a constant Mach number is achieved, the time step of LBM varies linearly with the grid size. The efficiency of LBM on the CM-5 parallel computer at the National Center for Supercomputing Applications (NCSA) is evaluated by examining each part of the algorithm. Overall, a speed of 13ċ9 GFLOPS is obtained using 512 processors for a domain size of 2176×2176.     

Development of a lattice Boltzmann method for two‐layered shallow‐water flow

In this paper the dynamics of a two‐layered liquid, made of two immiscible shallow‐layers of different density, has been investigated within the framework of the lattice Boltzmann method (LBM). The LBM developed in this paper for the two‐layered, shallow‐water flow has been obtained considering two separate sets of LBM equations, one for each layer. The coupling terms between the two sets have been defined as external forces, acted on one layer by the other. Results obtained from the LBM developed in this paper are compared with numerical results obtained solving the two‐layered, shallow‐water equations, with experimental and other numerical results published in literature. The results are interesting. First, the numerical results obtained by the LBM and by the shallow‐water model can be considered as equivalent. Second, the LBM developed in this paper is able to simulate motion conditions on nonflat topography. Third, the agreement between the LBM (and also shallow‐water model) numerical results and the experimental results is good when the evolution of the flow does not depend on the viscosity, that is, during the initial phase of the flow, dominated by gravity and inertia forces. When the viscous forces dominate the evolution of the flow the agreement between numerical and experimental results depends strongly on the viscosity; it is good if the numerical LBM viscosity has the same order of magnitude of the liquid's kinematic viscosity. Copyright © 2012 John Wiley & Sons, Ltd.     

Investigation on Heat and Mass Transfer in a Evaporator of a Capillary-Pumped Loop with the Lattice Boltzmann Method: Pore Scale Simulation

A two-dimensional transient numerical model based on the lattice Boltzmann method (LBM) for the global evaporator of a capillary-pumped loop (CPL) is proposed to describe heat and mass transfer with evaporation in the porous wick, heat conduction in the cover plate, and heat transfer in the vapor groove. To indicate the stochastic phase distribution characteristics of most porous wick, the quartet structure generation set (QSGS) is introduced for generating more realistic microstructures of porous media. By using the present lattice Boltzmann algorithm along with the porous structure, the heat and mass transfer of an evaporator on pore scale can be predicted without resorting to any empirical parameters determined case by case. The energy equations for entire evaporator are solved as a conjugate problem, which are solved by means of a spatially varying relaxation time in the lattice Boltzmann model and the liquid flow is driven via the interfacial mass flux. A convective boundary condition considering the latent heat during the evaporation on the interface is introduced into the lattice Boltzmann model based on the nonequilibrium extrapolation rule. Especially, the bounce-back rule and the equilibrium rule of the LBM are, respectively, introduced to deal with the momentum boundary conditions inside the porous wick and on the evaporation interface in order to ensure the stability and the efficiency of the LBM model. Numerical results corresponding to different working conditions and different working fluids are presented, which provide guidance for the evaporator design of a CPL system.     

LBM simulation of fluid flow in fractured porous media with permeable matrix

To analyze and depict complicated fluid behaviors in fractured porous media with variably permeable matrix, an integrated discrete computational algorithm is proposed based on lattice Boltzmann method (LBM). This paper combines with the external force model and statistical material physics to effectively describe the feature changes while the fluid passes through the fractures within the permeable matrix. As an application example, a two dimensional rock sample is reconstructed using the digital image and characterized with different feature values at each LBM grid to distinguish pores, impermeable and permeable matrix by stating its local physical property. Compared with the conventional LBM, the results demonstrate the advantages of proposed algorithm in modeling fluid flow phenomenon in fractured porous media with variably permeable matrix.