Lattice Boltzmann method for tempered time-fractional diffusion equation

In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation(ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.

Within the phase-field framework, we present an accurate and robust lattice Boltzmann (LB) method for simulating contact-line motion of immiscible binary fluids on the solid substrate. The most striking advantage of this method lies in that it enables us to handle two-phase flows with mass conservation and a high density contrast of 1000, which is often unavailable in the existing multiphase LB models. To simulate binary fluid flows, the present method utilizes two LB evolution equations, which are respectively used to solve the conservative Allen-Cahn equation for interface capturing, and the incompressible Navier-Stokes equations for hydrodynamic properties. Besides, to account for the substrate wettability, two popular contact angle models including the cubic surface-energy model and the geometrical one are incorporated into the present method, and their performances are numerically evaluated over a wide range of contact angles. The contact-angle hysteresis effect, which is inherent to a rough or chemically inhomogeneous substrate, is also introduced in the present LB approach through the strategy proposed by Ding and Spelt [J. Fluid Mech. 599, 341 (2008)10.1017/S0022112008000190]. The present method is first validated by simulating droplet spreading and capillary intrusion on the ideal or smooth pipes. It is found that the cubic surface-energy and geometrical wetting schemes both offer considerable accuracy for predicting a static contact angle within its middle region, while the former is more stable at extremely small contact angles. Besides, it is shown that the geometrical wetting scheme enables us to obtain better accuracy for predicting dynamic contact points in capillary pipe. Then we use the present LB method to simulate the droplet shearing processes on a nonideal substrate with contact angle hysteresis. The geometrical wetting model is found to be capable of reproducing four typical motion modes of contact line, while the surface-energy wetting scheme fails to predict the hysteresis behaviors in some cases. At last, a complex contact-line dynamic problem of three-dimensional microscale droplet impact on a wettable solid is simulated, and it is found that the numerical results for droplet shapes agree well with the experimental data.

ABSTRACTPrevious two-fluid lattice Boltzmann (LB) models for multicomponent fluids are limited to mixtures with a low molecular weight ratio (i.e., below 9). In this paper, a finite difference-based two-fluid LB model is developed for mixtures with larger molecular weight ratios, which can be widely found in real applications. The basic idea is to use the finite difference scheme to discretize the discrete velocity LB equations derived from the two-fluid theory. The corresponding macroscopic hydrodynamic and diffusion equations are obtained by multiscale expansions. The adjusting strategy of model parameters significantly influencing the accuracy and stability of the LB model is discussed in detail. It is demonstrated that the present LB method is able to model multicomponent fluids with a high molecular weight ratio (e.g., 32). Further, the present model is applied to the simulation of multicomponent fluids in porous media.

Lattice Boltzmann method for coupled radiation-conduction heat transfer in participating medium with graded-index

Peng-Robinson (P-R) equation of state (EOS) has been widely used in the petroleum industry for hydrocarbon fluids. In this work, a three-dimensional diffuse interface model with P-R EOS for two-phase fluid system is solved by the lattice Boltzmann (LB) method. In this diffuse interface model, an Allen-Cahn (A-C) type phase equation with strong nonlinear source term is derived. Using the multiscale Chapman-Enskog analysis, the A-C type phase equation can be recovered from the proposed LB method. Besides, a Lagrange multiplier is introduced based on the mesoscopic character of the LB scheme so that total mass of the hydrocarbon system is preserved. Three-dimensional numerical simulations of realistic hydrocarbon components, such as isobutane and propane, are implemented to illustrate the effectiveness of the proposed mass conservative LB scheme. Numerical results reach a better agreement with laboratory data compared to previous results of two-dimensional numerical simulations.

A lattice Boltzmann model for the conjugate heat transfer

Solving steady and transient radiative transfer problems with strong inhomogeneity via a lattice Boltzmann method

Simulation of two-phase fluid mixture flow in rectangular two-inlet cavity using lattice Boltzmann method

Surface tension plays a crucial role in governing interfacial dynamics during phase change phenomena spanning natural systems and industrial applications. The phase-field lattice Boltzmann (LB) method has emerged as a powerful approach for modeling phase change, particularly due to its inherent ability to capture interfacial tension effects in multiphase systems. However, there has been no three-dimensional phase-field LB method capable of simulating phase change initialed from a single-phase medium. In this study, we propose a phase-field-based LB method for modeling thermal phase change. A source term is derived to accurately describe phase change. A key distinguishing feature of our model is its capability to initiate phase change driven by the sensible heat of superheated or supercooled phases, thereby enabling the presence of superheated liquid and supercooled vapor. To validate the proposed model, we perform a series of benchmark tests using D3Q19 LB models with density ratios up to 1:1000. These include (i) a comparison between numerical results and analytical solutions of the one-dimensional Stefan problem and (ii) a quantitative evaluation of bubble departure diameter against the Fritz relation for bubble generation in a pure liquid phase under wall heating. The results demonstrate agreement with theoretical predictions, underscoring the accuracy and robustness of the proposed approach. This study extends the applicability of the LB method to scenarios requiring consideration of both surface tension and thermal phase change, offering a valuable tool for simulating complex multiphase systems.

In this paper, a comparative study of the lattice Boltzmann (LB) models for the Allen-Cahn (A-C) and Cahn-Hilliard (C-H) equations is conducted. To this end, a new LB model for the A-C equation is first proposed, where the equilibrium distribution function and the source term distribution function are delicately designed to recover the A-C equation correctly. The gradient term in this model can be computed by the nonequilibrium part of the distribution function such that the collision process can be implemented locally. Then a detailed numerical study on several classical problems is performed to give a comparison between the present model for the A-C equation and the recently developed LB model [H. Liang et al., Phys. Rev. E 89, 053320 (2014)PLEEE81539-375510.1103/PhysRevE.89.053320] for the C-H equation in terms of tracking the interface of two-phase flow. The results show that the present LB model for the A-C equation is more accurate and more stable, and also has a second-order convergence rate in space, while the convergence rate of the previous LB model for the C-H equation is only about 1.5.

The lattice Boltzmann (LB) method has been used to simulate rarefied gas flows in micro-systems as an alternative tool, and shown its application possibility. For the rarefied gas flows, the surface roughness plays an important role for the slip phenomenon at the wall. If the wall surface is sufficiently rough, the reflection of the molecules will be diffuse and the tangential momentum accommodation coefficient (TMAC) is equal to unity. However, it has been known that the reflections are not always fully diffuse. In this study, rarefied gas flows are simulated in the slip and the transition flow regime including the effect of the TMAC. For the simulations, new non-fully diffuse wall boundary treatments of the LB method are proposed. The results of 2D and 3D simulations are in excellent agreement with the analytical solutions for the slip flow regime. The solutions of the linearized Boltzmann equation and DSMC for the transition flow regime are compared with those of high order LB method with present boundary conditions, and they are in excellent agreement. The tangential momentum accommodation coefficient effect is also investigated.

Numerical simulations using the lattice Boltzmann (LB) method are presented for the two-dimensional channel flow with/without sudden expansion. Ninevelocity square lattice model is used. In order to improve computational efficiency of the LB method, nonuniform mesh is used, and residual averaging and mutigrid method are also incorporated into the LB method. By using these techniques, convergence to a steady state was considerably accelerated.

Lattice Boltzmann model for incompressible flows through porous media with time-fractional effects

Macrosegregation simulation model based on Lattice-Boltzmann method with high computational efficiency

Lattice Boltzmann modeling of wall-bounded ternary fluid flows