Numerical Methods For A Class Of Fluid-Structure Interaction Problems And Simulation Of Swaying Tree In Wind Field

A Class of fluid-structure interaction (FSI) problems with flexible structures immersed in fluid fields and fluid-structure interfaces between fluid and solid were studied in this paper and simulation of swaying trees in wind field were carried out based on the investigation of FSI numerical algorithms. Two typical numerical algorithms were deeply studied and some improvements were made to accommodate the simulation of swaying tree in wind field. A systematic simulation approach for swaying tree in wind field was proposed, and swaying behaviors of broad-leaf tree and no-leaf tree in wind field were simulated. The simulation method for wind-induced swaying tree simulation proposed in this paper was also implemented to physics-based animation generation.Two FSI algorithms that deeply studied were Arbitrary Lagrangian-Eulerian (ALE) method and Cartersian Cut Cell (CCC) method. For ALE method, a monolothic coupling approach and a mesh updating approach for valves in pipes was put forward, and 2D flow field near the leaf and the drag coefficient of the leaf was calculated using the similar approach. For CCC method, the original method was merely powerful for 2D problems, however some difficulties will meet due to the variety of cut cells when extending to 3D problems. Based on the requirement of wind-induced broad-leaf tree simulation, a simplified 3D CCC method is proposed in this paper by properly lower down the precision requirement in exchange of greatly lesson the cut cell types. The simplified method is much faster than the original one, and very suitable for wind-induced broad-leaf tree simulation.Based on the mended algorithms, a systematic approach of wind induced swaying tree simulation is proposed. This approach includes finite element tree model generation, estimation of material and aerodynamic property of tree leaves, different wind loading methods for broad-leaf tree and no-leaf tree, along with the FSI simulation methods for swaying trees in wind field. As an important part of the approach, a new method for calculating wind force exerting on the finite element broad-leaf tree model was given. The method was to establish a virtual shell structure as the fluid-structure interface surrounding the crown structure of the tree. Another important part of the approach is the two-way coupling simulation for no-leaf trees based on the experimental data of the fluctuating wind force on circular cylinders derived during the wind tunnel tests. The next point worth to mention was the investigation of a geometrically symmetric model for special purpose to investigate the influence of asymmetric material properties on tree motion.The simulation approach proposed in this paper was also applied to computer graphics field and a new method for physics-based animation generation based on the resulting database of wind-induced swaying tree simulation is proposed. Considering that animation generation needs massive data but the requirement of simulation precision is much lower than any engineering simulation, two effective methods were bring forward to accelerate the simulation: The first method was to run the one-way coupling code instead of two-way coupling code to save the time, but artificial damping was added to compensate the physical damping of two-way coupling algorithm, the amendment of artificial damping may prevent the dropping of simulation precision. The second method was named as "virtual material method", this method can enhance the time step size of explicit code of the dynamic finite element simulation by virtually adjusting the material parameters of tree material. The combination of simplified FS1 simulation method and virtual material method can greatly reduce the time for running the simulation, and meets the requirement of physics-based animation generation.