An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.

Data-driven optimization study of the multi-relaxation-time lattice Boltzmann method for solid-liquid phase change

Sharp phase interfaces and accurate temperature distributions are important criteria in the simulation of solid-liquid phase changes.The multi-relaxation-time lattice Boltzmann method(MRT-LBM)shows great numerical performance during simulation;however,the value method of the relaxation parameters needs to be specified.Therefore,in this study,a random forest(RF)model is used to discriminate the importance of different relaxation parameters to the convergence,and a support vector machine(SVM)is used to explore the decision boundary of the convergent samples in each dimensional model.The results show that the convergence of the samples is consistent with the sign of the decision number,and two types of the numerical deviations appear,i.e.,the phase mushy zone and the non-physical heat transfer.The relaxation parameters chosen on the decision boundary can further suppress the numerical bias and improve numerical accuracy.

A rescaling algorithm for multi-relaxation-time lattice Boltzmann method towards turbulent flows with complex configurations

Understanding and modeling flows over porous layers are of great industrial significance.To accurately solve the turbulent multi-scale flows on complex configurations,a rescaling algorithm designed for turbulent flows with the Chapman-Enskog analysis is proposed.The mesh layout and the detailed rescaling procedure are also introduced.Direct numerical simulations(DNSs)for a turbulent channel flow and a porous walled turbulent channel flow are performed with the three-dimensional nineteen-velocity(D3Q19)multiple-relaxation-time(MRT)lattice Boltzmann method(LBM)to validate the accuracy,adaptability,and computational performance of the present rescaling algorithm.The results,which are consistent with the previous DNS studies based on the finite difference method and the LBM,demonstrate that the present method can maintain the continuity of the macro values across the grid interface and is able to adapt to complex geometries.The reasonable time consumption of the rescaling procedure shows that the present method can accurately calculate various turbulent flows with multi-scale and complex configurations while maintaining high computational efficiency.

Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM)

The lattice Boltzmann method （LBM） is used to examine free convection of nanofluids. The space between the cold outer square and heated inner circular cylinders is filled with water including various kinds of nanoparticles： TiO2, Ag, Cu, and A1203. The Brinkman and Maxwell-Garnetts models are used to simulate the viscosity and the effective thermal conductivity of nanofluids, respectively. Results from the performed numerical analysis show good agreement with those obtained from other numerical meth- ods. A variety of the Rayleigh number, the nanoparticle volume fraction, and the aspect ratio are examined. According to the results, choosing copper as the nanoparticle leads to obtaining the highest enhancement for this problem. The results also indicate that the maximum value of enhancement occurs at λ =2.5 when Ra = 106 while at A = 1.5 for other Rayleigh numbers.

NEW STUDYING OF LATTICE BOLTZMANN METHOD FOR TWO-PHASE DRIVEN IN POROUS MEDIA

By using the interaction of particles, such as the physical principle of the same attract each other and the different repulse each other, a new model of Lattice Boltzmann to simulate the two-phase driven in porous media was discussed. The result shows effectively for the problem of two-phase driven in porous media. Furthermore, the method economizes on computer time, has less fluctuation on boundary surface and takes no average measure.

Study on Free Surface and Channel Flow Induced by Low Temperature Plasma via Lattice Boltzmann Method

Active boundary layer flow control and boundary layer manipulation in the channel flow that was based on low temperature plasma were studied by means of a lattice Boltzmann method. Two plasma actuators were placed in a row to obtain the influence rule of their separation distance on the velocity profile at three locations and maximum velocity in the flow field. Two plasma actuators were placed symmetrically inside a channel to examine the effect of channel height and voltage on the velocity profile and flow rate. It was found that the channel height controls the distribution of flow velocity, which affected the flow rate and its direction. Increasing plasma voltage had a negative effect on the flow rate due to the generation of a larger and stronger flow vortex.

Numerical simulation of dynamic process for liquid film spreading by lattice Boltzmann method and its experimental verification

Combined with the kinetic model of liquid film spreading,a new numerical method of solid-liquid-gas three-phase flow was developed for the moving of contact line,which was a hybrid method of computational fluid dynamics and lattice Boltzmann method(LBM).By taking the effect of molecule force in droplet and the wall surface on liquid film into account,the changing law of contact angle with different surface tensions was analyzed on glass and aluminum foil surfaces.Compared with experimental results,the standard deviation by using LBM is less than 0.5°,which validates the feasibility of LBM simulation on the dynamic process of liquid film spreading.In addition,oscillations are discovered both at the initial and end phases.The phenomenon of retraction is also found and the maximum retraction angle is 7.58°.The obtained result shows that the retraction is proved to be correlative with precursor film by tracking the volume change of liquid film contour.Furthermore,non-dimensional coefficient λ is introduced to measure the liquid film retraction capacity.

Airfoil design optimization based on lattice Boltzmann method and adjoint approach

We present a new aerodynamic design method based on the lattice Boltzmann method （LBM） and the adjoint approach. The flow field and the adjoint equation are numerically simulated by the GILBM （generalized form of interpolation supplemented LBM） on non-uniform meshes. The first-order approximation for the equilibrium dis- tribution function on the boundary is proposed to diminish the singularity of boundary conditions. Further, a new treatment of the solid boundary in the LBM is described par- ticularly for the airfoil optimization design problem. For a given objective function, the adjoint equation and its boundary conditions are derived analytically. The feasibility and accuracy of the new approach have been perfectly validated by the design optimization of NACA0012 airfoil.

High velocity flow simulation using lattice Boltzmann method with no-free-parameter dissipation scheme

A finite difference lattice Boltzmann method of second-order accuracy in time is developed based on non-oscillatory scheme with no-free-parameter dissipation （NND） difference scheme in this paper. The NND lattice Boltzmann method is used to simulate high-speed flows by constructing a new equilibrium distribution function of the lattice Boltzmann method. Compared with a variation of lattice Boltzmann method developed by Qu, et al., the present method can capture shock waves and handle oscillations of high velocity flows accurately in larger time steps and in shorter computing time. Numerical results indicate the correctness and capability of simulating shock wave interactions of the NND lattice Boltzmann method.

基于lattice Boltzmann方法对裂隙煤体中瓦斯运移规律的模拟研究

基于lattice Boltzmann方法建立一个新的模拟裂隙煤体内瓦斯渗流的动力学模型,并利用该模型模拟二维裂隙煤体内瓦斯流动。模拟结果表明,采动压力差对瓦斯流动速度、孔隙瓦斯压力及瓦斯压力梯度都有很大的影响。在采动压力条件下,瓦斯在裂隙煤体中的流动压力具有波动性,波动幅度的大小与流场两端的压力差有关。在瓦斯压力达到峰值前的瞬时,孔隙瓦斯压力梯度很大。随着采动压力差的增大,瓦斯流动由层流过渡到紊流,同时孔隙压力出现发散,压力变化出现明显的非线性特征。基于lattice Boltzmann方法的模拟结果与用其他方法得到的瓦斯渗流规律比较吻合,表明lattice Boltzmann方法可有效模拟瓦斯在裂隙煤体中的运移规律,这为进一步探讨煤与瓦斯两相耦合机制、煤与瓦斯突出机制及瓦斯抽放方案的设计提供新的思路。

双重网格的Lattice Boltzmann方法

针对均匀网格的LatticeBoltzmann方法(LBM)计算效率较低的不足,引入有限差分方法(FDM)中双重网格算法的基本思想,结合LBM在连续流场上变量也连续分布的特点,推导出双重网格的LBM.这种算法充分利用粗、细两种网格各自不同的优点,加快了收敛速度,提高了流场的计算效率.通过模拟二维Poiseulle流动和后台阶流动两个算例,证明双重网格算法的计算时间明显地少于均匀网格算法的计算时间,计算结果正确可信.

Lattice Boltzmann方法不同边界条件的混用

在Lattice Boltzmann方法数值模拟中,比较重要的一个环节就是边界条件的确定.通过对不同边界条件混用情况的研究,发现不同的边界条件确定方法可以相互混用,说明了Lattice Bolt-zmann方法对于边界的处理是比较灵活的.

Simulation of two-phase flows of a droplet impacting on a liquid film with an improved lattice Boltzmann model

Based on the lattice Boltzmann method（LBM）,an improved pseudo-potential model,combined with a method of adding force term,is used to simulate the two-phase flows caused by a liquid droplet impacting on a liquid film.In this model,the different phases are treated as one fluid,and the interfaces between the vapor and liquid phases can be obtained by density value of the fluid.This variant of the LBM allows one to obtain the densities of vapor and liquid with high accuracy.The model is validated by an example of phase separation.The early stage of the impact of droplet on liquid film is simulated,and the results are qualitatively consistent with physical phenomena.

Lattice Boltzmann simulations of turbulent shear flow between parallel porous walls

The effects of two parallel porous walls are investigated, consisting of the Darcy number and the porosity of a porous medium, on the behavior of turbulent shear flows as well as skin-friction drag. The turbulent channel flow with a porous surface is directly simulated by the lattice Boltzmann method （LBM）. The Darcy-Brinkman- Forcheimer （DBF） acting force term is added in the lattice Boltzmann equation to simu- late the turbulent flow bounded by porous walls. It is found that there are two opposite trends （enhancement or reduction） for the porous medium to modify the intensities of the velocity fluctuations and the Reynolds stresses in the near wall region. The parametric study shows that flow modification depends on the Darcy number and the porosity of the porous medium. The results show that, with respect to the conventional impermeable wall, the degree of turbulence modification does not depend on any simple set of param- eters obviously. Moreover, the drag in porous wall-bounded turbulent flow decreases if the Darcy number is smaller than the order of O（10-4） and the porosity of porous walls is up to 0.4.

Boundary scheme for lattice Boltzmann modeling of micro-scale gas flow in organic-rich pores considering surface diffusion

We propose a boundary scheme for addressing multi-mechanism flow in a porous medium in slip and early transition flow regimes, which is frequently encountered in shale gas reservoirs. Micro-gaseous flow in organic-rich shale involves a complex flow mechanism. A self-developed boundary scheme that combines the non-equilibrium extrapolation scheme and the combined diffusive reflection and bounce-back scheme(half-way DBB) to embed the Langmuir slip boundary into the single-relaxation-time lattice Boltzmann method(SRT-LBM) enables us to describe this process, namely, the coupling effect of micro-gaseous flow and surface diffusion in organic-rich nanoscale pores. The present LBM model comes with the careful consideration of the local Knudsen number, local pressure gradient, viscosity correction model, and regularization procedure to account for the rarefied gas flows in irregular pores. Its validity and accuracy are verified by several benchmarking cases, and the calculated results by this boundary scheme accord well with our analytical solutions.This boundary scheme shows a higher accuracy than the existing studies. Additionally, a subiteration strategy is presented to tackle the coupled micro-gaseous flow and surface diffusion, which necessitates the iteration process matching of these two mechanisms. The multi-mechanism flow in the self-developed irregular pores is also numerically investigated and analyzed over a wide range of parameters. The results indicate that the present model can effectively capture the coupling effect of micro-gaseous flow and surface diffusion in a tree-like porous medium.

Lattice Boltzmann simulation of MHD natural convection in a cavity with porous media and sinusoidal temperature distribution

The lattice Boltzmann method(LBM) is used to simulate the effect of magnetic field on the natural convection in a porous cavity. The sidewalls of the cavity are heated sinusoidally with a phase derivation, whereas the top and bottom walls are thermally insulated. Numerical simulation is performed, and the effects of the pertinent parameters, e.g., the Hartmann number, the porosity, the Darcy number, and the phase deviation, on the fluid flow and heat transfer are investigated. The results show that the heat transfer is affected by the temperature distribution on the sidewalls clearly. When the Hartmann number is 0, the maximum average Nusselt number is obtained at the phase deviation 90?. Moreover, the heat transfer enhances when the Darcy number and porosity increase, while decreases when the Hartman number increases.

Comparative study of two lattice Boltzmann multiphase models for simulating wetting phenomena: implementing static contact angles based on the geometric formulation

Wetting phenomena are widespread in nature and industrial applications. In general, systems concerning wetting phenomena are typical multicomponent/multiphase complex fluid systems. Simulating the behavior of such systems is important to both scientific research and practical applications. It is challenging due to the complexity of the phenomena and difficulties in choosing an appropriate numerical method. To provide some detailed guidelines for selecting a suitable multiphase lattice Boltzmann model, two kinds of lattice Boltzmann multiphase models, the modified S-C model and the H-C-Z model, are used in this paper to investigate the static contact angle on solid surfaces with different wettability combined with the geometric formulation(Ding, H. and Spelt, P.D. M. Wetting condition in diffuse interface simulations of contact line motion. Physical Review E, 75(4), 046708(2007)). The specific characteristics and computational performance of these two lattice Boltzmann method(LBM) multiphase models are analyzed including relationship between surface tension and the control parameters, the achievable range of the static contact angle, the maximum magnitude of the spurious currents(MMSC), and most importantly, the convergence rate of the two models on simulating the static contact angle. The results show that a wide range of static contact angles from wetting to non-wetting can be realized for both models. MMSC mainly depends on the surface tension. With the numerical parameters used in this work, the maximum magnitudes of the spurious currents of the two models are on the same order of magnitude. MMSC of the S-C model is universally larger than that of the H-C-Z model. The convergence rate of the S-C model is much faster than that of the H-C-Z model. The major foci in this work are the frequently-omitted important details in simulating wetting phenomena. Thus, the major findings in this work can provide suggestions for simulating wetting phenomena with LBM multiphase models along with the geometric formulation.

Lattice Boltzmann simulation of natural convection in open end cavity with inclined hot wall

Natural convection in an open end cavity with a hot inclined wall is simulated based on the lattice Boltzmann method （LBM）. The physics of flow and energy transfer in open end cavities are addressed when the hot wall is inclined. The combination of the two topics （open cavity and inclined walls） is the main novelty of the present study. The effects of the angle of the hot inclined wall on the flow field and heat transfer are thoroughly investigated. The Prandtl number is fixed to 0.71 （air）. The Rayleigh number and the angle of the hot inclined wall are varied in the range of 10^4 to 10^6 and 60° to 85°, respectively. The results are presented for two different aspect ratios, i.e., A = 1 and 2. The results obtained with the LBM are also compared with those of the finite volume method （FVM）. The predicted results of the LBM conform to those of the FVM. The results show that by increasing the angle of the hot inclined wall and the aspect ratio of the cavity, the average Nusselt number decreases. The trend of the local Nusselt number on the inclined wall is also discussed.

A particle-resolved heat-particle-fluid coupling model by DEM-IMB-LBM

Multifield coupling is frequently encountered and also an active area of research in geotechnical engineering.In this work,a particle-resolved direct numerical simulation(PR-DNS)technique is extended to simulate particle-fluid interaction problems involving heat transfer at the grain level.In this extended technique,an immersed moving boundary(IMB)scheme is used to couple the discrete element method(DEM)and lattice Boltzmann method(LBM),while a recently proposed Dirichlet-type thermal boundary condition is also adapted to account for heat transfer between fluid phase and solid particles.The resulting DEM-IBM-LBM model is robust to simulate moving curved boundaries with constant temperature in thermal flows.To facilitate the understanding and implementation of this coupled model for non-isothermal problems,a complete list is given for the conversion of relevant physical variables to lattice units.Then,benchmark tests,including a single-particle sedimentation and a two-particle drafting-kissing-tumbling(DKT)simulation with heat transfer,are carried out to validate the accuracy of our coupled technique.To further investigate the role of heat transfer in particle-laden flows,two multiple-particle problems with heat transfer are performed.Numerical examples demonstrate that the proposed coupling model is a promising high-resolution approach for simulating the heat-particle-fluid coupling at the grain level.

An MPI parallel DEM-IMB-LBM framework for simulating fluid-solid interaction problems

The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive computational costs.To overcome this limitation,a message passing interface(MPI)parallel DEM-IMB-LBM framework is proposed aimed at enhancing computation efficiency.This framework utilises a static domain decomposition scheme,with the entire computation domain being decomposed into multiple subdomains according to predefined processors.A detailed parallel strategy is employed for both contact detection and hydrodynamic force calculation.In particular,a particle ID re-numbering scheme is proposed to handle particle transitions across sub-domain interfaces.Two benchmarks are conducted to validate the accuracy and overall performance of the proposed framework.Subsequently,the framework is applied to simulate scenarios involving multi-particle sedimentation and submarine landslides.The numerical examples effectively demonstrate the robustness and applicability of the MPI parallel DEM-IMB-LBM framework.