Search Results (8)

A mesoscopic lattice Boltzmann method based on the BGK model is proposed to solve a class of two-dimensional second-order nonlinear partial differential equations by incorporating an amending function. The model provides an efficient and stable framework for simulating initial value problems of second-order nonlinear partial differential equations and is adaptable to various nonlinear systems, including strongly nonlinear cases. The numerical characteristics and evolution patterns of these nonlinear equations are systematically investigated. A D2Q4 lattice model is employed, and the kinetic moment constraints for both local equilibrium and correction distribution functions are derived in the four velocity directions. Explicit analytical expressions for these distribution functions are presented. The model is verified to recover the target macroscopic equations in the continuous limit via Chapman–Enskog analysis. Numerical experiments using exact solutions are performed to assess the model’s accuracy and stability. The results show excellent agreement with exact solutions and demonstrate the model’s robustness in capturing nonlinear dynamics. Full article

Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws. PINNs open up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar–Gross–Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts equilibrium control equations in different discrete velocity directions within the SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling the inference of the fluid’s non-equilibrium characteristics. The third component, a physics-informed function, translates the outputs of the first two networks into physical information. By minimizing the residuals of the physical partial differential equations (PDEs), the physics-informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models that are applicable to different dimensions, named the PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physics-informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into a neural network through the interpretation function. Therefore, the PINN-SRT-LBM allows a given neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Our experimental results confirm the accurate prediction by this model of flow information at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently. Full article

A modified thermal Bhatnagar–Gross–Krook Lattice Boltzmann (BGK-LB) model was developed to study the convection phenomenon of non-Newtonian fluids (NNFs). This model integrates the local shear rate into the equilibrium distribution function (EDF) of the flow field and keeps the relaxation time from varying with fluid viscosity by introducing an additional parameter. In addition, a modified temperature EDF was constructed for the evolution equation of the temperature field to ensure the precise recovery of the convection–diffusion equation. To validate the accuracy and effectiveness of the proposed model, numerical simulations of benchmark problems were performed. Subsequently, we investigated the natural convection of power–law (PL) fluids and examined the impact of the PL index (n = 0.7–1.3) and Rayleigh number (Ra = 10³–5 × 10⁵) on the flow and temperature fields while holding the Prandtl number (Pr = 7) constant. The obtained results indicate that, for a given value of n, the convective intensity exhibits a positive correlation with Ra, which is illustrated by the rising trend in the average Nusselt number ($\overline{Nu}$) with increasing Ra. Additionally, shear-thinning fluid (n < 1) exhibited increased $\overline{Nu}$ values compared to the Newtonian case, indicating an enhanced convection effect. Conversely, shear-thickening fluid (n > 1) exhibits reduced $\overline{Nu}$ values, indicating weakened convective behavior. Full article

This work presents a new approach to investigating water conduction properties in real three-dimensional (3D) voids of asphalt mixtures. Three different molding methods were employed for the same grade of asphalt mixture, and the three asphalt mixture specimens were scanned using X-ray Computerized Tomography (CT) to identify the real 3D void structure distribution inside the mixture. The real 3D behavior of void moisture conduction inside the mixture was simulated using the discrete lattice Boltzmann method and the BGK collision model. Three different molding methods were used to study the behavior of mesoscopic seepage inside the specimen. The results show that water conduction varies substantially in real 3D voids inside diverse molded objects. Regardless of flow and flow velocity, the Superpave Gyratory Compactor (SGC) method is extraordinarily close to the conduction qualities of the actual field core material. It shows that the Marshall molding method is inconsistent with the actual pavement molding method, and the SGC method can not only ensure that the reasonable void ratio is conducive to the thermal expansion and cold shrinkage space of the asphalt mixture but also prevents rainwater from entering the asphalt mixture. This work provides a new perspective for the study of water damage resistance and medium transmission characteristics of asphalt mixtures. Full article

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations. Full article

The pseudopotential Lattice Boltzmann Method has attracted much attention in the recent years for the simulation of boiling heat transfer. Many studies have been published recently for the simulation of the bubble cycle (nucleation, growth and departure from a heated surface). This paper puts forward two-dimensional simulations of bubble nucleation, growth and departure using an improved pseudopotential Lattice Boltzmann Model from the literature at different reduced temperatures, $T_r=0.76$ and $T_r=0.86$. Two different models using the Bhatnagar–Gross–Krook (BGK) and the Multiple-Relaxation-Time (MRT) collision operators with appropriate forcing schemes are used. The results for pool boiling show that the bubbles exhibit axial symmetry during growth and departure. Numerical results of departure diameter and release period for pool boiling are compared against empirical correlations from the literature by varying the gravitational acceleration. Reasonable agreement is observed. Nucleate boiling trends with heat flux are also captured by the simulations. Numerical results of flow boiling simulations are compared by varying the Reynolds number for both reduced temperatures with the MRT model. It was found that the departure diamenter and release period decreases with the increase of the Reynolds number. These results are a direct effect of the drag force. Proper conclusions are commented at the end of the paper. Full article

In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate local equilibrium distribution functions. We validate the present mesoscopic model by some related issues where the exact solution is known. It turned out that the numerical solution is in very good agreement with exact one, which shows that the present mesoscopic model is pretty valid, and can be used to solve more similar nonlinear wave equations with nonlinear damping and source terms, and predict and enrich the internal mechanism of nonlinearity and complexity in nonlinear dynamic phenomenon. Full article

The surface characteristics, such as wettability and roughness, play an important role in heat transfer performance in the field of microfluidic flow. In this paper, the process of a hot liquid flowing through a microchannel with cold walls, which possesses different surface wettabilities and microstructures, is simulated by a transient double-distribution function (DDF) two-phase thermal lattice Boltzmann BGK (LBGK) model. The Shan-Chen multiphase LBGK model is used to describe the flow field and the independent distribution function is introduced to solve the temperature field. The simulation results show that the roughness of the channel wall improves the heat transfer, no matter what the surface wettability is. These simulations reveal that the heat exchange characteristics are directly related to the flow behavior. For the smooth-superhydrophobic-surface flow, a gas film forms that acts as an insulating layer since the thermal conductivity of the gas is relatively small in comparison to that of a liquid. In case of the rough-superhydrophobic-surface flow, the vortex motion of the gas within the grooves significantly enhances the heat exchange between the fluid and wall. Full article