Three-dimensional cascaded lattice Boltzmann method: Improved implementation and consistent forcing scheme

Generalized equilibria for color-gradient lattice Boltzmann model based on higher-order Hermite polynomials: A simplified implementation with central moments

We propose generalized equilibria of a three-dimensional color-gradient lattice Boltzmann model for two-component two-phase flows using higher-order Hermite polynomials. Although the resulting equilibrium distribution function, which includes a sixth-order term on the velocity, is computationally cumbersome, its equilibrium central moments (CMs) are velocity-independent and have a simplified form. Numerical experiments show that our approach, as in Wen et al. [Phys. Rev. E 100, 023301 (2019)2470-004510.1103/PhysRevE.100.023301] who consider terms up to third order, improves the Galilean invariance compared to that of the conventional approach. Dynamic problems can be solved with high accuracy at a density ratio of 10; however, the accuracy is still limited to a density ratio of 1000. For lower density ratios, the generalized equilibria benefit from the CM-based multiple-relaxation-time model, especially at very high Reynolds numbers, significantly improving the numerical stability.

Pore-Scale Study on Convective Drying of Porous Media

In this work, a numerical model for isothermal liquid-vapor phase change (evaporation) of the two-component air-water system is proposed based on the pseudopotential lattice Boltzmann method. Through the Chapman-Enskog multiscale analysis, we show that the model can correctly recover the macroscopic governing equations of the multicomponent multiphase system with a built-in binary diffusion mechanism. The model is verified based on the two-component Stefan problem where the measured binary diffusivity is consistent with theoretical analysis. The model is then applied to convective drying of a dual-porosity porous medium at the pore scale. The simulation captures a classical transition in the drying process of porous media, from the constant rate period (CRP, first phase) showing significant capillary pumping from large to small pores, to the falling rate period (FRP, second phase) with the liquid front receding in small pores. It is found that, in the CRP, the evaporation rate increases with the inflow Reynolds number (Re), while in the FRP, the evaporation curves almost collapse at different Res. The underlying mechanism is elucidated by introducing an effective Péclet number (Pe). It is shown that convection is dominant in the CRP and diffusion in the FRP, as evidenced by Pe > 1 and Pe < 1, respectively. We also find a log-law dependence of the average evaporation rate on the inflow Re in the CRP regime. The present work provides new insights into the drying physics of porous media and its direct modeling at the pore scale.

Unified lattice Boltzmann method with improved schemes for multiphase flow simulation: Application to droplet dynamics under realistic conditions

As a powerful mesoscale approach, the lattice Boltzmann method (LBM) has been widely used for the numerical study of complex multiphase flows. Recently, Luo et al. [Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 379, 20200397 (2021)10.1098/rsta.2020.0397] proposed a unified lattice Boltzmann method (ULBM) to integrate the widely used lattice Boltzmann collision operators into a unified framework. In this study, we incorporate additional features into this ULBM in order to simulate multiphase flow under realistic conditions. A nonorthogonal moment set [Fei et al., Phys. Rev. E 97, 053309 (2018)10.1103/PhysRevE.97.053309] and the entropic-multi-relaxation-time (KBC) lattice Boltzmann model are used to construct the collision operator. An extended combined pseudopotential model is proposed to realize multiphase flow simulation at high-density ratio with tunable surface tension over a wide range. The numerical results indicate that the improved ULBM can significantly decrease the spurious velocities and adjust the surface tension without appreciably changing the density ratio. The ULBM is validated through reproducing various droplet dynamics experiments, such as binary droplet collision and droplet impingement on superhydrophobic surfaces. Finally, the extended ULBM is applied to complex droplet dynamics, including droplet pancake bouncing and droplet splashing. The maximum Weber number and Reynolds number in the simulation reach 800 and 7200, respectively, at a density ratio of 1000. The study demonstrates the generality and versatility of ULBM for incorporating schemes to tackle challenging multiphase problems.

Droplet evaporation in finite-size systems: Theoretical analysis and mesoscopic modeling

The classical D^{2}-Law states that the square of the droplet diameter decreases linearly with time during its evaporation process, i.e., D^{2}(t)=D_{0}^{2}-Kt, where D_{0} is the droplet initial diameter and K is the evaporation constant. Though the law has been widely verified by experiments, considerable deviations are observed in many cases. In this work, a revised theoretical analysis of the single droplet evaporation in finite-size open systems is presented for both two-dimensional (2D) and 3D cases. Our analysis shows that the classical D^{2}-Law is only applicable for 3D large systems (L≫D_{0}, L is the system size), while significant deviations occur for small (L≤5D_{0}) and/or 2D systems. Theoretical solution for the temperature field is also derived. Moreover, we discuss in detail the proper numerical implementation of droplet evaporation in finite-size open systems by the mesoscopic lattice Boltzmann method (LBM). Taking into consideration shrinkage effects and an adaptive pressure boundary condition, droplet evaporation in finite-size 2D/3D systems with density ratio up to 328 within a wide parameter range (K=[0.003,0.18] in lattice units) is simulated, and remarkable agreement with the theoretical solution is achieved, in contrast to previous simulations. The present work provides insights into realistic droplet evaporation phenomena and their numerical modeling using diffuse-interface methods.

A unified lattice Boltzmann model and application to multiphase flows

In this work, we develop a unified lattice Boltzmann model (ULBM) framework that can seamlessly integrate the widely used lattice Boltzmann collision operators, including the Bhatnagar-Gross-Krook or single-relation-time, multiple-relaxation-time, central-moment or cascaded lattice Boltzmann method and multiple entropic operators (KBC). Such a framework clarifies the relations among the existing collision operators and greatly facilitates model comparison and development as well as coding. Importantly, any LB model or treatment constructed for a specific collision operator could be easily adopted by other operators. We demonstrate the flexibility and power of the ULBM framework through three multiphase flow problems: the rheology of an emulsion, splashing of a droplet on a liquid film and dynamics of pool boiling. Further exploration of ULBM for a wide variety of phenomena would be both realistic and beneficial, making the LBM more accessible to non-specialists. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Cross-platform programming model for many-core lattice Boltzmann simulations

We present a novel, hardware-agnostic implementation strategy for lattice Boltzmann (LB) simulations, which yields massive performance on homogeneous and heterogeneous many-core platforms. Based solely on C++17 Parallel Algorithms, our approach does not rely on any language extensions, external libraries, vendor-specific code annotations, or pre-compilation steps. Thanks in particular to a recently proposed GPU back-end to C++17 Parallel Algorithms, it is shown that a single code can compile and reach state-of-the-art performance on both many-core CPU and GPU environments for the solution of a given non trivial fluid dynamics problem. The proposed strategy is tested with six different, commonly used implementation schemes to test the performance impact of memory access patterns on different platforms. Nine different LB collision models are included in the tests and exhibit good performance, demonstrating the versatility of our parallel approach. This work shows that it is less than ever necessary to draw a distinction between research and production software, as a concise and generic LB implementation yields performances comparable to those achievable in a hardware specific programming language. The results also highlight the gains of performance achieved by modern many-core CPUs and their apparent capability to narrow the gap with the traditionally massively faster GPU platforms. All code is made available to the community in form of the open-source project stlbm, which serves both as a stand-alone simulation software and as a collection of reusable patterns for the acceleration of pre-existing LB codes.

Linear stability and isotropy properties of athermal regularized lattice Boltzmann methods

The present work proposes a general methodology to study stability and isotropy properties of lattice Boltzmann (LB) schemes. As a first investigation, such a methodology is applied to better understand these properties in the context of regularized approaches. To this extent, linear stability analyses of two-dimensional models are proposed: the standard Bhatnagar-Gross-Krook collision model, the original precollision regularization, and the recursive regularized model, where off-equilibrium distributions are partially computed thanks to a recursive formula. A systematic identification of the physical content carried by each LB mode is done by analyzing the eigenvectors of the linear systems. Stability results are then numerically confirmed by performing simulations of shear and acoustic waves. This work allows drawing fair conclusions on the stability properties of each model. In particular, among the aforementioned models, recursive regularization turns out to be the most stable one for the D2Q9 lattice, especially in the zero-viscosity limit. Two major properties shared by every regularized model are highlighted: (1) a mode filtering property and (2) an incorrect, and broadly anisotropic, dissipation rate of the modes carrying physical waves in under-resolved conditions. The first property is the main source of increased stability, especially for the recursive regularization. It is a direct consequence of the reconstruction of off-equilibrium populations before each collision process, decreasing the rank of the system of discrete equations. The second property seems to be related to numerical errors directly induced by the equilibration of high-order moments. In such a case, this property is likely to occur with any collision model that follows such a stabilization methodology.

Central-Moments-Based Lattice Boltzmann for Associating Fluids: A New Integrated Approach

Dynamic and thermodynamic behaviors of associating fluids play a crucial role in various science and engineering disciplines. Cubic plus association equation of state (CPA EOS) is implemented in a central-moments-based lattice Boltzmann method (LBM) in order to mimic the thermodynamic behavior of associating fluids. The pseudopotential approach is selected to model the multiphase thermodynamic characteristics such as reduced density of associating fluids. The priority of central-moments-based approach over multiple-relaxation-time collision operator is highlighted by performing double shear layers. The integration of central-moments-based LBM and CPA EOS is useful to simulate the dynamic and thermodynamic characteristics of associating fluids at high flow rate conditions, which is extended to high-density ratio scenarios by increasing the anisotropy order of gradient operator. In order to increase the stability of the model, a higher anisotropy order of the gradient operator is implemented; about 34 present reduction in spurious velocities is noticed in some cases. The type of gradient operator considerably affects the model thermodynamic consistency. Finally, the model is validated by observing a straight line in the Laplace law test. Prediction of thermodynamic behaviors of associating fluids is of significance in various applications including biological processes as well as fluid flow in porous media.

Discrete fluidization of dense monodisperse emulsions in neutral wetting microchannels

The rheology of pressure-driven flows of two-dimensional dense monodisperse emulsions in neutral wetting microchannels is investigated by means of mesoscopic lattice Boltzmann simulations, capable of handling large collections of droplets, in the order of several hundreds. The simulations reveal that the fluidization of the emulsion proceeds through a sequence of discrete steps, characterized by yielding events whereby layers of droplets start rolling over each other, thus leading to sudden drops of the relative effective viscosity. It is shown that such discrete fluidization is robust against loss of confinement, namely it persists also in the regime of small ratios of the droplet diameter over the microchannel width. We also develop a simple phenomenological model which predicts a linear relation between the relative effective viscosity of the emulsion and the product of the confinement parameter (global size of the device over droplet radius) and the viscosity ratio between the disperse and continuous phases. The model shows excellent agreement with the numerical simulations. The present work offers new insights to enable the design of microfluidic scaffolds for tissue engineering applications and paves the way to detailed rheological studies of soft-glassy materials in complex geometries.

Comprehensive comparison of collision models in the lattice Boltzmann framework: Theoretical investigations

Over the last decades, several types of collision models have been proposed to extend the validity domain of the lattice Boltzmann method (LBM), each of them being introduced in its own formalism. This article proposes a formalism that describes all these methods within a common mathematical framework, and in this way allows us to draw direct links between them. Here, the focus is put on single and multirelaxation time collision models in either their raw moment, central moment, cumulant, or regularized form. In parallel with that, several bases (nonorthogonal, orthogonal, Hermite) are considered for the polynomial expansion of populations. General relationships between moments are first derived to understand how moment spaces are related to each other. In addition, a review of collision models further sheds light on collision models that can be rewritten in a linear matrix form. More quantitative mathematical studies are then carried out by comparing explicit expressions for the post-collision populations. Thanks to this, it is possible to deduce the impact of both the polynomial basis (raw, Hermite, central, central Hermite, cumulant) and the inclusion of regularization steps on isothermal LBMs. Extensive results are provided for the D1Q3, D2Q9, and D3Q27 lattices, the latter being further extended to the D3Q19 velocity discretization. Links with the most common two and multirelaxation time collision models are also provided for the sake of completeness. This work ends by emphasizing the importance of an accurate representation of the equilibrium state, independently of the choice of moment space. As an addition to the theoretical purpose of this article, general instructions are provided to help the reader with the implementation of the most complicated collision models.

Lattice-Boltzmann Simulations of Electrowetting Phenomena

When a voltage difference is applied between a conducting liquid and a conducting (solid) electrode, the liquid is observed to spread on the solid. This phenomenon, generally referred to as electrowetting, underpins a number of interfacial phenomena of interest in applications that range from droplet microfluidics to optics. Here, we present a lattice-Boltzmann method that can simulate the coupled hydrodynamics and electrostatics equations of motion of a two-phase fluid as a means to model the electrowetting phenomena. Our method has the advantage of modeling the electrostatic fields within the lattice-Boltzmann algorithm itself, eliminating the need for a hybrid method. We validate our method by reproducing the static equilibrium configuration of a droplet subject to an applied voltage and show that the apparent contact angle of the drop depends on the voltage following the Young-Lippmann equation up to contact angles of ≈50°. At higher voltages, we observe a saturation of the contact angle caused by the competition between electric and capillary stresses, similar to previous experimental observations. We also study the stability of a dielectric film trapped between a conducting fluid and a solid electrode and find a good agreement with analytical predictions based on lubrication theory. Finally, we investigate the film dynamics at long times and report observations of film breakup and entrapment similar to previously reported experimental results.

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework

The cascaded lattice Boltzmann method decomposes the collision stage on a basis of central moments on which the equilibrium state is assumed equal to that of the continuous Maxwellian distribution. Such a relaxation process is usually considered as an assumption, which is then justified a posteriori by showing the enhanced Galilean invariance of the resultant algorithm. An alternative method is to relax central moments to the equilibrium state of the discrete second-order truncated distribution. In this paper, we demonstrate that relaxation to the continuous Maxwellian distribution is equivalent to the discrete counterpart if higher-order (up to sixth) Hermite polynomials are used to construct the equilibrium when the D3Q27 lattice velocity space is considered. Therefore, a theoretical a priori justification of the choice of the continuous distribution is formally provided for the first time.

Color-gradient lattice Boltzmann model with nonorthogonal central moments: Hydrodynamic melt-jet breakup simulations

We develop a lattice Boltzmann (LB) model for immiscible two-phase flow simulations with central moments (CMs). This successfully combines a three-dimensional nonorthogonal CM-based LB scheme [De Rosis, Phys. Rev. E 95, 013310 (2017)2470-004510.1103/PhysRevE.95.013310] with our previous color-gradient LB model [Saito, Abe, and Koyama, Phys. Rev. E 96, 013317 (2017)2470-004510.1103/PhysRevE.96.013317]. Hydrodynamic melt-jet breakup simulations show that the proposed model is significantly more stable, even for flow with extremely high Reynolds numbers, up to O(10^{6}). This enables us to investigate the phenomena expected under actual reactor conditions.