Numerical Simulation Of Free-surface Flows Based On The Lattice Boltzmann Method

A free-surface is the interface between at least two different fluids, such as water-gas free-surface. The difficulty of the simulation of free-surface flow lies in how to handle the interaction between difference phases. If not handled properly, non-physical phenomena, such as pseudo-oscillation, may occur near the interface, leading to the decrease of stability and accuracy. Moreover, the so called numerical dissipation effect, arising from the artificial viscosity brought by numerical methods, may make sharp interface smooth, which decreases the resolution of the interface. Therefore, the free-surface problem has always been a major issue in the field of Computational Fluid Dynamics(CFD).Free-surface flows exist in a wide range of real life and engineering fields, such as droplets and bubbles related problems, ocean waves, filling processes and so on. Thorough understanding about free-surface flows facilitates the generation of new technologies, mak-ing a great convenience for the improvement of fluid-related equipment. Therefore, research on free-surface flows is very meaningful.In order to simulate free-surface flow accurately and efficiently, researchers have al-ways been making efforts. As a result, a great many methods with their own merits and weaknesses have been developed. All these methods can be sorted into three categories:ex-perimental method, analytical method and numerical method. Among the three categories, numerical method has emerged as the major research method with the rapid development of computer. Currently, the main traditional numerical methods are finite difference method, finite volume method and finite element method. In recent years, because of its simple im-plementation, natural parallelism and the ability to handle complex boundaries with ease, the lattice Boltzmann method(LBM) has emerged as a promising method for fluid flows and endured a great development. LBM is also extended to multiphase flows. Unfortunately, current multiphase models in LBM cannot deal with fluid flows with a big density ratio and viscosity ratio, such as free-surface flows. To attack this issue, two lattice Boltzmann based single-phase free-surface models have been proposed.Our work is based on one of the single-phase free-surface models. The main contents of this thesis are:(1) On the basis of a single-phase free-surface model in the lattice Boltzmann method(LB-SP), we propose an improved model to treat surface tension and wall adhesion.To remove the weaknesses in the surface tension model of LB-SP and the latter im-proved model, we propose an improved surface tension and wall adhesion model for free- surface flows in the lattice Boltzmann method by introducing conservative surface tension model in conventional CFD and the corresponding wall adhesion model. Some numerical cases-the deformation of a square droplet, flows induced by wall adhesion and surface ten-sion, and filling processes in a2D cavity-are carried out to verify the effectiveness of the current model. Results show that the surface tension and wall adhesion model in present study can simulate surface tension isotropically and achieve desired wetting properties by setting static contact angles. In the end, filling processes in a2D cavity shows similar pat-terns as those in literatures, which suggests the effectiveness of the present free-surface model.(2) Combine the particle level set method and the lattice Boltzmann method(LB-PLSM), and develop a new hybrid method with higher precision.Since level set kind method is more accurate than Volume of Fluid kind method, by combining the particle level set method and the lattice Boltzmann method(LB-PLSM), we develop a new hybrid method with higher precision for free-surface flows and simulate the process of an initially square fluid patch. Results show that this coupled model has good performance on mass conservation.(3) Make a detailed comparative study of LB-PLSM and LB-SP.We implement the LB-PLSM model to simulate the evolution of an initially circular fluid patch and the classical breaking dam case. Numerical results by LB-PLSM are com-pared with experimental results and the results by LB-SP, which shows that LB-PLSM has better accuracy but lower efficiency than LB-SP. If higher accuracy is required, LB-PLSM is a better choice. On the other hand, LB-PLSM and LB-SP are also carried out to simulate the breaking dam splash problems. Results suggest that both method show good performance on the simulation of complex free-surface flows. Since both methods are single-phase method, they cannot capture the influence of gas on liquid.(4) Couple Ghost fluid with LB-PLSM, develop a hybrid model for free-surface flows with moving solid boundaries, and make a preliminary verification of this model.We propose a hybrid Ghost fluid and LB-PLSM model for free-surface flows with moving solid boundaries, and implement this model to simulate water exit, sinking of a submerged cylinder and water entry problems. Results show that current model can simulate free-surface with moving solid boundaries but need further study.