Numerical Methods Based On LBM For Two-phase Flows With Surfactant And Two Kinds Of Complex FSI Problems

Fluid-structure-interaction (FSI) problems and multi-phase flow with surfactant are found in many science and engineering applications, the interaction between fluid and structure plays a key role in the dynamic stability of structure and the characteristics of flow field, and the presence of surfactant in fluid have a considerable effect on the in-terface and dynamics of flow. With the urgent demands in numerical calculation and simulations of these two kinds of complex problems, it is more and more important to devise efficient algorithms, which also presents many challenges. Currently, the main numerical method for present problems is partitioned approaches. In present work, sev-eral decoupling methods based on LBM are studied for the problems including flapping filament, swimming jellyfish and two-phase flow with surfactant. The main contents of the dissertation are as follows:Flapping filament has a strong background in the fields of biology kinematics. Aim-ing at this problem, a momentum exchange-based IB-LBM (denoted as ME-IB-LBM for convenience) is constructed:IB-LBM, imbibing advantages of both methods, is applied to solve the flow field, and the interaction force between fluid and structure is calculated by using the concept of momentum exchange, which overcomes the drawback of the penalty method employing a user-defined spring parameter. Then, a single flapping fila-ment in the flow field is simulated with different resolution grids, and numerical results show that ME-IB-LBM is stable and convergent. Furthermore, several typical flapping filament problems are simulated. Our numerical results are consistent quantitatively with physical phenomena in laboratory experimental, and the effects of mass density and the gap between the two filaments on flapping filament and the characteristics of flow field are consistent with previous theoretical results and numerical results. On this basis, the effects of filament length and flexure modulus are studied, and some new results are ob-tained, which have an important value to analyze the mechanism of fluid-flexible-body-interaction.Swimming jellyfish is a kind of FSI problems with voluntary locomotion, and this study can promote deep analysis on working principles of jet propulsion. Aiming at this problem, an appropriate ME-IB-LBM is constructed. Then, an oblate jellyfish is simulated with different resolution grids, and numerical results show that the constructed ME-IB- LBM is stable and convergent. Furthermore, a lot of numerical simulations are given based on2D and3D jellyfish-models. Our numerical results are consistent quantitatively with physical phenomena in laboratory experimental, and the effects of Reynolds number on the swimming jellyfish and characteristics of flow field are consistent with previous theoretical results and numerical results. Furthermore, some new findings are obtained by studying the effects of jellyfish mass density, which provide a meaningful guidance in the field of industrial design, such as thrusters and jet engine.The convection-diffusion process on moving surface with surfactant is an indispens-able problem for studying multi-phase flow with surfactant. Aiming at this problem, an semi-implicit finite difference scheme based on a Level Set Method (denoted as LS-SIFD scheme for convenience) is was first proposed:the Level Set Method is adopted to capture interface and extend surfactant concentration off interface; the semi-implicit Crank-Nicholson scheme is employed for the time discretization; the diffusion term is dis-cretized by central difference scheme, while the convective term is discretized by WENO scheme. The stability analysis shows that LS-SIFD is stable with standard Courant-Friedrichs-Lewy conditions. Meanwhile, Numerical results validate that present algo-rithm has second order accuracy and good conservative.Two-phase flows with surfactant are very complex fluid problems. Aiming at this problem, a new composition algorithm based on LS-SIFD scheme is given (denoted as LS-II-LBM scheme for convenience) with the flow field solved by Lattice Boltzmann Method and Immersed Interface Method. Meanwhile, a strategy to improve conservation is provided. Then, a single drop with surfactant in shear flow is simulated with different resolution grids, and numerical results show that LS-II-LBM has a good approximation, stability and conservation. Furthermore, the effect of equation of state, Capillary num-ber, Peclet number, Reynolds number, surfactant coverage and viscosity ratio on drop shape and distribution of surfactant concentration, surface tension, capillary force and Marangoni force are studied, and the results are consistent with previous numerical re-sults.