Boltzmann Model Research Articles

Global existence for an isotropic modification of the Boltzmann equation

Motivated by the open problem of large-data global existence for the non-cutoff Boltzmann equation, we introduce a model equation that in some sense disregards the anisotropy of the Boltzmann collision kernel. We refer to this model equation as isotropic Boltzmann by analogy with the isotropic Landau equation introduced by Krieger and Strain (2012) [35]. The collision operator of our isotropic Boltzmann model converges to the isotropic Landau collision operator under a scaling limit that is analogous to the grazing collisions limit connecting (true) Boltzmann with (true) Landau.Our main result is global existence for the isotropic Boltzmann equation in the space homogeneous case, for certain parts of the “very soft potentials” regime in which global existence is unknown for the space homogeneous Boltzmann equation. The proof strategy is inspired by the work of Gualdani and Guillen (2022) [22] on isotropic Landau, and makes use of recent progress on weighted fractional Hardy inequalities.

Development of a cascaded lattice Boltzmann model for two‐layer shallow water flows

SummaryMany environmental phenomena, such as flows in rivers or in coastal region can be characterised by means of the ‘shallow approach’. A multi‐layer scheme allows to extend it to density layered shallow water flows (e.g., gravity currents). Although a variety of models allowing numerical investigation of single and multi‐layer shallow water flows, based on continuum and particle approaches, have been widely discussed, there are still some computational aspects that need further investigation. Focusing on the Lattice Boltzmann models (LBM), available multi‐layer models generally use the standard linear collision operator (CO). In this work we adopt a multi relaxation time (MRT) cascaded collision operator to develop a two‐layered liquid Lattice‐Boltzmann model (CaLB‐2). Specifically, the model solves the shallow water equations, taking into account two separate sets of particle distribution function (PDF), one for each layer, solved separately. Layers are connected through coupling terms, defined as external forces that model the mutual actions between the two layers. The model is validated through comparisons with experimental and numerical results from test cases available in literature. First results are very promising, highlighting a good correspondence between simulation results and literature benchmarks.

Numerical Simulation for Solitary Waves of the Generalized Zakharov Equation Based on the Lattice Boltzmann Method

The generalized Zakharov equation is a widely used and crucial model in plasma physics, which helps to understand wave particle interactions and nonlinear wave propagation in plasma. The solitary wave solution of this equation provides insights into phenomena such as electron and ion acoustic waves, as well as magnetic field disturbances in plasma. The numerical simulation of solitary wave solutions to the generalized Zakharov equation is an interesting problem worth studying. This is crucial for plasma-based technology, as well as for understanding nonlinear wave propagation in plasma physics and other fields. In this study, a numerical investigation of the generalized Zakharov equation using the lattice Boltzmann method has been conducted. The lattice Boltzmann method is a new modeling and simulating method at the mesoscale. A lattice Boltzmann model was constructed by performing Taylor expansion, Chapman–Enskog expansion, and time multiscale expansion on the lattice Boltzmann equation. By defining the moments of the equilibrium distribution function appropriately, the macroscopic equation can be restored. Furthermore, the numerical experiments for the equation are carried out with the parameter lattice size m=100, time step Δt=0.001, and space step size Δx=0.4. The solitary wave solution of the equation is numerically simulated. Numerical results under different parameter values are compared, and the convergence and effectiveness of the model are numerically verified. It is obtained that the model is convergent in time and space, and the convergence orders are all 2.24881. The effectiveness of our model was also verified by comparing the numerical results of different numerical methods. The lattice Boltzmann method demonstrates advantages in both accuracy and CPU time. The results indicate that the lattice Boltzmann method is a good tool for computing the generalized Zakharov equation.

Effect of the angle of wedge-shaped hydrophilic patterns on drop evaporation and contact line behaviour: A lattice Boltzmann study

Hypothesis:Angular hydrophilic patterns can manipulate the drop morphology for applications like inkjet-printing. It is hypothesized that such patterns can also affect the contact line behaviour and evaporation rate of drops in a dynamic way, further affecting the quality of depositions. Here, the effect of the angular region is quantified using a wedge-shaped pattern. Experiments:The pseudo-potential multicomponent lattice Boltzmann (LB) model is used for the diffusion-limited (isothermal) evaporation of pinned liquid drops from wedge-shaped hydrophilic patterns. Findings:The contact line unpins the earliest at the apex region of the smallest wedge angles due to a pronounced difference between the local and overall contact angles. The difference reduces linearly with increasing wedge angles, leading to their delayed unpinning. The evaporative flux along the contact line is initially independent of the contact angle but reduces sharply near the unpinning angle. The variation of flux across wedge angles depends more on unpinning timings, as maximum flux values did not differ significantly. The evaporation rate is dynamic, with the smaller wedge angles initially exhibiting a higher evaporation rate because of larger drop surface areas, while the larger wedge angles dominate later owing to the delayed unpinning and retaining larger drop surface areas.

Simulation of phase change during the freezing of unsaturated porous media by using a coupled lattice Boltzmann model

PurposeThe purpose of this paper is to develop a coupled lattice Boltzmann model for the simulation of the freezing process in unsaturated porous media.Design/methodology/approachIn the developed model, the porous structure with complexity and disorder was generated by using a stochastic growth method, and then the Shan-Chen multiphase model and enthalpy-based phase change model were coupled by introducing a freezing interface force to describe the variation of phase interface. The pore size of porous media in freezing process was considered as an influential factor to phase transition temperature, and the variation of the interfacial force formed with phase change on the interface was described.FindingsThe larger porosity (0.2 and 0.8) will enlarge the unfrozen area from 42 mm to 70 mm, and the rest space of porous medium was occupied by the solid particles. The larger specific surface area (0.168 and 0.315) has a more fluctuated volume fraction distribution.Originality/valueThe concept of interfacial force was first introduced in the solid–liquid phase transition to describe the freezing process of frozen soil, enabling the formulation of a distribution equation based on enthalpy to depict the changes in the water film. The increased interfacial force serves to diminish ice formation and effectively absorb air during the freezing process. A greater surface area enhances the ability to counteract liquid migration.

A Boltzmann model equation synchronously involving molecular internal energy, dissociation and recombination effects for multicomponent gases

On the basis of previous work, we propose a phenomenological computable Boltzmann model equation synchronously involving polyatomic molecular internal energies, dissociation and recombination effects for multicomponent gases in this paper. Here, the distribution functions of each species have nine independent variables, which are time, physical space, molecular velocity, rotational energy and vibrational energy, if this component is a polyatomic gas. In this model equation, the concept of ‘chemical reaction rate’ is introduced in the chemical collision term to characterize the affect of chemical reactions. In order to make this complex model equation being ‘computable’, reduced distribution functions are adopted to get rid of two independent variables about rotational energy and vibrational energy of polyatomic component. We prove the conservation of this model equation, and then numerically solve it by the framework of gas-kinetic unified algorithm (GKUA), which is one kind of discrete velocity method (DVM). Here, non-catalytic boundary condition is adopted. Finally, a simple hypersonic flow around a cylinder with Mach number being 24.85 is numerically simulated to verify this model equation. In this case, four different components and eight chemical reactions are considered. It is shown that, this proposed Boltzmann model equation has the potential to be used to simulate thermochemical non-equilibrium effects of hypersonic flows covering various regimes.

A lattice Boltzmann model for incompressible gas and liquid two-phase flows combined with free-surface method

A novel lattice Boltzmann (LB) model is proposed to study the gas and liquid two-phase flows with large density and viscosity ratios. In the model, both the gas and liquid phases are considered as viscous incompressible fluids, which are governed separately by the two-relaxation-time LB equations. They are coupled by a momentum exchange method at the interface. The interaction between the gas and liquid phases is explicitly described and naturally involved in the model. The interfacial conditions in the model are validated by the benchmarks of the layered Poiseuille flow and the Laplace law. The feasibility of combining this model with the bubble model and the wetting scheme is proven through transient flow problems of single bubble rising and capillary intrusion. The validity of this model is confirmed by more complex flows including solid–liquid–gas coupling and droplet breaking problems by simulating shearing a droplet on a substrate and a droplet falling on a liquid film. The results demonstrate that the present model can be used to describe both the gas and the liquid flows. This work provides a solution to model the simulation of the dynamical behaviors of multi-phase flows.

Lattice Boltzmann modeling of convective heat and solute transfer in additive manufacturing of multi-component alloys

Additive manufacturing (AM) is a remarkable breakthrough technology, allowing for the direct fabrication of three-dimensional components through the layer-by-layer stacking of materials. A novel free Surface lattice Boltzmann (LB) model is developed to simulate the heat and solute transfer in AM of multi-component alloys. The behavior liquid phase is described by using the free surface LB model, and the phase transitions between solid and liquid are modeled by using the LB-enthalpy method. A LB equation is directly constructed, which accounts for solute transfer in a certain multi-component alloys system. The thermodynamic information used in the calculation of phase transitions are determined by an extensive thermodynamic database. The model is validated via several benchmark examples of fluid flow and heat transfer. The characteristics of convective heat and solute transfer within various AM are investigated. Finally, the non-equilibrium convective heat transfer, phase transitions, and macroscopic segregation are discussed within the AM melt pools. The melt pool expands and convective heat transfer is enhanced by the Marangoni effect. Thus there is a consistent decrease in solute segregation. The solute segregation is more severe near the surface of the deposit layer. Additionally, the thermal convection experiences cyclic intensification attributed to the successive impact of multiple droplets in wire feeding and melting AM. This continuous impact serves to diminish the solute segregation. The results underscore the significant potential and advantages of LB method in accurately simulating the AM, which provides valuable insights for understanding the underlying mechanism of heat and solute transfer in materials and manufacturing.

The droplet race: Optimization of a wettability gradient surface

Droplet behavior influenced by wettability distribution is a pertinent field of research with applications in lab-on-a-chip and heat transfer devices among others. Some have proposed patterned surfaces with controlled variation of wettability to orient the direction of the droplet motion or to increase its velocity. These patterns are arrived upon with experience and knowledge of this phenomenon. In this research paper, the authors used a mathematical approach to the physical problem by using a gradient based optimizer for maximizing droplet velocity. Given some initial conditions, the optimizer marches toward the optimum wettability distribution profile. The droplet motion is modeled in two dimensions (i.e., on the xy-plane), on a plate having a wettability distribution in one dimension (i.e., along the x axis). The single component pseudopotential model allows for the quantification of the wettability distribution as a distribution of a pseudodensity of the solid nodes of the flat plate. Starting with several monotonous analytical profiles, a quadratic convex profile allows us to reach the maximum mean velocity for the threshold droplet displacement. Different sets of initial profiles, length of the plate (L), and diameter of the droplet (D) are tested. For smaller L/D ratio, the optimal wettability distributions exhibit non-trivial features: profiles can be non-monotonous, and wettability gradient could be locally null. With the increase in the L/D ratio, these specificities tend to be less prominent and optimal profiles converge to the quadratic convex one. The main innovation and significance of the paper is that mathematical optimization algorithms have been used conjointly with a multiphase lattice Boltzmann model solver to address for the first time the droplet race defined as: “what is the best wettability profile in order for a droplet to reach a desired location as quickly as possible?”

High-order thread-safe lattice Boltzmann model for high performance computing turbulent flow simulations

We present a highly optimized thread-safe lattice Boltzmann model in which the non-equilibrium part of the distribution function is locally reconstructed via recursivity of Hermite polynomials. Such a procedure allows the explicit incorporation of non-equilibrium moments of the distribution up to the order supported by the lattice. Thus, the proposed approach increases accuracy and stability at low viscosities without compromising performance and amenability to parallelization with respect to standard lattice Boltzmann models. The high-order thread-safe lattice Boltzmann is tested on two types of turbulent flows, namely, the turbulent channel flow at Reτ=180 and the axisymmetric turbulent jet at Re = 7000; it delivers results in excellent agreement with reference data [direct numerical simulations (DNS), theory, and experiments] and (a) achieves peak performance [∼5×1012 floating point operations (FLOP) per second and an arithmetic intensity of ∼7 FLOP/byte on a single graphic processing unit] by significantly reducing the memory footprint, (b) retains the algorithmic simplicity of standard lattice Boltzmann computing, and (c) allows to perform stable simulations at vanishingly low viscosities. Our findings open attractive prospects for high-performance simulations of realistic turbulent flows on GPU-based architectures. Such expectations are confirmed by excellent agreement among lattice Boltzmann, experimental, and DNS reference data.

Investigation of oil/water two-phase flow behavior in laminated shale porous media considering heterogeneous structure and fluid-solid interaction

The laminated structure of continental shale oil reservoirs introduces significant macro and micro heterogeneity, posing challenges for efficient shale oil extraction. Existing microscopic experimental and simulation methods are insufficient to accurately simulate the fluid flow behavior in mud–lime interactive laminated shale reservoirs. This study delves into the complexities of laminated shale reservoirs with a focus on their heterogeneous structure and wettability. Using scanning electron microscopy, we extracted the structural features of laminated shale reservoirs and established a Multicomponent and multiphase -multi relaxation time-Lattice Boltzmann model(MCMP-MRT-LBM) that considers nanoscale effects such as wall adsorption, liquid–solid slippage, and liquid–liquid slippage. We investigated the occurrence state, the flow behavior, and the phase seepage characteristics of crude oil in laminated shale at different water saturation stages and explored the reasons behind interlayer channeling and the conditions under which crude oil is mobile within limestone and mudstone layers. Then, we examined the impact of varying factors, including heterogeneous wettability, displacement pressure gradients, and pore size, on relative permeability, water injection capacity, sweep efficiency, and crude oil recovery in laminated reservoirs. The results indicate that wettability and pore size distribution, driven by capillary and viscous forces, dictate the occurrence state of remaining oil. Wettability primarily influences fluid distribution, whereas pore size distribution substantially impacts fluid morphology. It also highlights the pivotal role of flow velocity differences between layers in causing interlayer channeling. Increasing the capillary number promotes crude oil mobility within mudstone layers, with the initiation pressure gradient in mudstone layers being 2.5 times that of the limestone layer. The examination of the oil–water relative permeability reveals the dominance of pressure gradients in affecting oil flow capabilities, while pore size significantly influences water flow capacity. By optimizing various factors, it is possible to enhance water injection capacity and sweep efficiency, resulting in a substantial 5%–10% increase in crude oil recovery from laminated shale reservoirs.

Numerical investigation of flow past a cylinder using cumulant lattice Boltzmann method

This paper presents simulations of flow past a circular cylinder within the subcritical Reynolds number (Re) range from 3900 to 2 × 105, utilizing the parameterized cumulant lattice Boltzmann model. In this study, a three-dimensional characteristic boundary condition for incompressible flow has been integrated into the lattice Boltzmann method at the outflow boundary to minimize spurious reflection. The flow field, wake statistics, hydrodynamic force, and power spectra results of Re = 3900 from the cumulant lattice Boltzmann model are exhaustively compared with the laboratory data and other numerical models. Relative to other numerical models employing turbulence closure, the cumulant lattice Boltzmann simulations demonstrate enhanced agreement with the experimental data even with relatively coarser grid resolution. The resolution-spanning feature for the cumulant lattice Boltzmann model in turbulent flows, without using explicit turbulence model, aligns with the previous benchmark case studies. The stability-preserving regularization process in the present model is analyzed. Results indicate that the influence of the regularization parameter is mitigated with improved grid resolution. A specific regularization parameter for flow around cylinder simulations is recommended. Variations in flow properties and hydrodynamic forces within the subcritical Reynolds number range of 3900 to 2 × 105 are analyzed. The results confirm that the parameterized cumulant lattice Boltzmann model can accurately simulate practical engineering flows, characterized by complex separation and recirculation, within the subcritical range. Moreover, the computational efficiency and parallel scalability are compared with other numerical methods.

A thermal lattice Boltzmann model for evaporating multiphase flows

Modeling thermal multiphase flows has become a widely sought methodology due to its scientific relevance and broad industrial applications. Much progress has been achieved using different approaches, and the lattice Boltzmann method is one of the most popular methods for modeling liquid–vapor phase change. In this paper, we present a novel thermal lattice Boltzmann model for accurately simulating liquid–vapor phase change. The proposed model is built based on the equivalent variant of the temperature governing equation derived from the entropy balance law, in which the heat capacitance is absorbed into transient and convective terms. Then a modified equilibrium distribution function and a proper source term are elaborately designed in order to recover the targeting equation in the incompressible limit. The most striking feature of the present model is that the calculations of the Laplacian term of temperature, the gradient term of temperature, and the gradient term of density can be simultaneously avoided, which makes the formulation of the present model is more concise in contrast to all existing lattice Boltzmann models. Several benchmark examples, including droplet evaporation in open space, droplet evaporation on a heated wall, and nucleate boiling phenomenon, are carried out to assess numerical performance of the present model. It is found that the present model effectively improves the numerical accuracy in solving the interfacial behavior of liquid–vapor phase change within the lattice Boltzmann method framework.

Effect of heating wires with electric potential on pool-boiling heat transfer under an electric field

In this study, we investigated the influence of heating wires with electric potential on a pool-boiling system under an electric field. We employed a numerical method that combines the pseudopotential lattice Boltzmann model, leaky dielectric model, and finite-difference model. Heating wires with different positions and electric potentials above a horizontal heater were explored. A detailed analysis of the boiling process occurring on the heater was performed at various electric-field intensities and for different boiling regimes, both with and without wires. For the pool-boiling system without heating wires, the results revealed that the critical heat flux (CHF) increased with the electric-field intensity, and the superheat required for the system to attain film boiling increased with electric field intensity. Placing heating wires on the heater surface resulted in the deterioration of heat transfer in the system without an electric field. However, the optimal distance between the heating wires and the heater remarkably promoted heat transfer during the film-boiling regime. The introduction of heating wires with electric potential into the system disrupted the original electric-field distribution, consequently impacting the boiling process and heat transfer. Compared with the system without both heating wires and an electric field, the system without heating wires exhibited a 7.9 % increase in the largest CHF at a low electric-field intensity of CaE = 0.2. However, at the same electric-field intensity, the largest CHF increased by up to 39.4 % when heating wires with an electric potential were employed. These findings provide a theoretical foundation for the practical application of effectively employing wires with electric potential to enhance boiling heat transfer.

Droplet evaporation on two-tier hierarchical micro-pillar array surface

As surface modification becomes a promising approach to thermal management, quantifying effects of surface structure geometrical dimension is of great significance to optimize heat transfer performance. In this paper, we emphatically report droplet evaporation on three types of two-tier hierarchical micro-pillar array (THM) surfaces. Utilizing the lattice Boltzmann model, evaporation characteristics including droplet morphology, triple-phase contact line (TPCL) behavior, liquid–vapor interface evolution and heat flux distribution are elucidated. In comparison to single-tier micro-pillar array (SM) surfaces, THM surfaces enable remarkable enhancement in heat transfer when secondary pillars are configured on the side of the primary pillar or configured parallelly to the primary pillar on the substrate, which is attributed to the synergistic effect of TPCL evaporation and liquid–vapor interface evaporation. The varying trend of droplet lifetime with the primary pillar geometrical dimension on all THM surfaces are also summarized, giving a guideline for optimization of heat dissipation by tailoring structures.

Numerical investigations on the droplet moving in steam with non-condensable gas by lattice Boltzmann method

Spray cooling is an efficient cooling technology with high heat dissipation, and has been extensively utilized in various industry areas. The interaction mechanism between the spray droplet and environmental space with high pressure and temperature is extremely complex, especially with non-condensable gas. In this paper, a pseudopotential multicomponent multiphase lattice Boltzmann model for droplet migration with non-condensable gas in high temperature and pressure was proposed. The mechanism of transfer characteristics for droplet in steam were studied. It is found that the mass transfer of droplet is controlled by density and condensation, droplet growth is mainly impacted by density at initial stage, and in later period, the growth is greatly weakened by the condensation suppression of non-condensable gas. The calculated results show that when Fo > 0.4, mass transfer is significantly decreased. Heat transfer is also affected by non-condensable gas, and 2% gas declines the droplet heat transfer rate by about 10%. It is also found that the mass transfer rate is approximately linearly associated with the ratio of non-condensable gas content inside and outside the droplet. The results can be used for development of spray cooling model, and have positive guiding significance for optimizing spray cooling system.

An effective and robust lattice Boltzmann model guided by atlas for hippocampal subregions segmentation.

Given the varying vulnerability of the rostral and caudal regions of the hippocampus to neuropathology in the Alzheimer's disease (AD) continuum, accurately assessing structural changes in these subregions is crucial for early AD detection. The development of reliable and robust automatic segmentation methods for hippocampal subregions (HS) is of utmostimportance. Our aim is to propose and validate a HS segmentation model that is both training-free and highly generalizable. This method should exhibit comparable accuracy and efficiency to state-of-the-art techniques. The segmented HS can serve as a biomarker for studying the progression ofAD. We utilized the functional magnetic resonance imaging of the Brain's Integrated Registration and Segmentation Tool (FIRST) to segment the entire hippocampus. By intersecting the segmentation results with the Brainnetome (BN) atlas, we obtained coarse segmentation of the four HS regions. This coarse segmentation was then employed as a shape prior term in the lattice Boltzmann (LB) model, as well as for initializing contours. Additionally, image gradients and local gray levels were integrated into the external force terms of the LB model to refine the coarse segmentation results. We assessed the segmentation accuracy of the model using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and evaluated the potential of the segmentation results as AD biomarkers on both the ADNI and Xuanwudatasets. The median Dice similarity coefficients (DSC) for the left caudal, right caudal, left rostral, and right rostral hippocampus were 0.87, 0.88, 0.88, and 0.89, respectively. The proportion of segmentation results with a DSC exceeding 0.8 was 77%, 78%, 77%, and 94% for the respective regions. In terms of volume, the correlation coefficients between the segmentation results of the four HS regions and the gold standard were 0.95, 0.93, 0.96, and 0.96, respectively. Regarding asymmetry, the correlation coefficient between the segmentation result's right caudal minus left caudal and the corresponding gold standard was 0.91, while for right rostral minus left rostral, it was 0.93. Over time, we observed a decline in the volumes of the four HS regions and the total hippocampal volume of mild cognitive impairment (MCI) converters. Analysis of inter-group differences revealed that, except for the right rostral region in the ADNI dataset, the p-values for the four HS regions in the normal controls (NC), MCI, and AD groups from both datasets were all below 0.05. The right caudal hippocampal volume demonstrated correlation coefficients of 0.47 and 0.43 with the mini-mental state examination (MMSE) and Montreal cognitive assessment (MoCA), respectively. Similarly, the left rostral hippocampal volume showed correlation coefficients of 0.50 and 0.58 with MMSE and MoCA,respectively. Our framework allows for direct application to different brain magnetic resonance (MR) datasets without the need for training. It eliminates the requirement for complex image preprocessing steps while achieving segmentation accuracy comparable to deep learning (DL) methods even with small sample sizes. Compared to traditional active contour models (ACM) and atlas-based methods, our approach exhibits significant speed advantages. The segmented HS regions hold promise as potential biomarkers for studying the progression ofAD.

Lattice Boltzmann modeling of buoyant convection in an enclosure with differentially heated porous cylinders

This study employs the Lattice Boltzmann Method, utilizing the Darcy-Brinkmann-Forchheimer model, to investigate buoyancy-driven heat transfer within an enclosure featuring differentially heated porous cylinders. The enclosure comprises two isothermal cylinders (one hot and one cold) separated by a distance within a cooled enclosure. It comprehensively assesses the impact of Darcy numbers ranging from 10-6 to 10-2, Rayleigh numbers spanning from 104 to 106, and various cylinder orientations. Specifically, five distinct configurations are considered, including horizontal alignment of hot and cold cylinders (Case A), vertical alignment of hot and cold cylinders (Cases B & C), and diagonal alignment of hot and cold cylinders (Cases D & E). The key findings highlight that the highest heat dissipation occurs in proximity to the heated cylinder, with certain orientations consistently demonstrating superior heat dissipation. The study explores the heat and flow characteristics at different Rayleigh numbers, examining these through streamlines and isotherms. Also, the impact of cylinder permeability on heat transfer features is comprehensively analyzed and reported. The findings of this research offer valuable insights for optimizing the placement of electronic components within compact electronic cabinets, with potential benefits for electronic cooling and thermal management.

Phase-field lattice Boltzmann model with singular mobility for quasi-incompressible two-phase flows.

In this paper, a lattice Boltzmann for quasi-incompressible two-phase flows is proposed based on the Cahn-Hilliard phase-field theory, which can be viewed as an improved model of a previous one [Yang and Guo, Phys. Rev. E 93, 043303 (2016)2470-004510.1103/PhysRevE.93.043303]. The model is composed of two LBE's, one for the Cahn-Hilliard equation(CHE) with a singular mobility, and the other for the quasi-incompressible Navier-Stokes equations(qINSE). Particularly, the LBE for the CHE uses an equilibrium distribution function containing a free parameter associated with the gradient of chemical potential, such that the variable (and even zero) mobility can be handled. In addition, the LBE for the qINSE uses an equilibrium distribution function containing another free parameter associated with the local shear rate, such that the large viscosity ratio problems can be handled. Several tests are first carried out to test the capability of the proposed LBE for the CHE in capturing phase interface, and the results demonstrate that the proposed model outperforms the original LBE model in terms of accuracy and stability. Furthermore, by coupling the hydrodynamic equations, the tests of double-stationary droplets and droplets falling problems indicate that the proposed model can reduce numerical dissipation and produce physically acceptable results at large time scales. The results of droplets falling and phase separation of binary fluid problems show that the present model can handle two-phase flows with large viscosity ratio up to the magnitude of 10^{4}.

Enhanced cascaded lattice Boltzmann model for multiphase flow simulations at large density ratio

In recent years, the pseudopotential multiphase lattice Boltzmann method (LBM) has been widely applied in the numerical simulations of complex multiphase flow. However, numerical stability at high Weber (We) and Reynolds (Re) numbers seriously restricts its application. In the present work, the pseudopotential multiphase LBM is developed by introducing the entropic stabilizers to the cascaded collision operator, and thus, the numerical stability is effectively enhanced. The relaxation rates for different order moments are all determined by fluid viscosities and the maximum entropy condition instead of being user-defined. Furthermore, the surface tension and contact angle can be adjusted in a wide range, which extends the application of the pseudopotential multiphase model. The accuracy and capability of the present model to simulate the complex multiphase flow are validated by reproducing the droplet impact on the flat or textured superhydrophobic surfaces. In addition, a droplet impact on the superhydrophobic surface at We=1280 and Re=18000 is simulated, in which the Weber and Reynolds numbers have significantly increased. This strongly demonstrates that the present model can enhance the numerical stability in the simulation of large density ratio multiphase flows at simultaneously high Weber and Reynolds numbers, which means the present model can further extend the pseudopotential multiphase LBM to more realistic scientific and technical applications.