楊德良2006-07-252018-07-092006-07-252018-07-092004http://ntur.lib.ntu.edu.tw//handle/246246/2874The mail purpose of the present study aims at the establishment of a numerical model for a nonlinear 3D free surface flows with the emphasis on the vortical structure. In order to comprehend the motion of the fluid flows, the Navier-Stokes equations through the velocity-vorticity formulation are adopted to deal with free surface flows. The governing equations for the velocity field are deduced to the linear Poisson equations which will be solved by the finite element method (FEM). The governing equations of vorticity field are the vorticity transport equations. As far as solution of vorticity is concerned, we have successfully developed a finite element method (FEM) model to attack the advection-diffusion-reaction equation. In the free-surface boundary conditions, the kinematic boundary conditions are imposed on the free surface positions, while the velocity on the free surfaces is solved by using the free surface dynamic boundary conditions. While analyzing a three-dimensional problem, there are a lot of data to be handled during the calculating process. Although the calculating power of computer is now advancing, it still costs a lot of time to compute. In order to increase the efficiency of computation, the present research work will investigate parallel computation techniques for finite element analysis. It is more important to discuss that the motion of incompressible flows with free surface flows are solved by the finite element method using Velocity-Vorticity formulation. In tradition, the most investigators solve free surface floe problems using primitive variable methods or vorticity-stream function method, so it is very difficult to attempt the velocity-vorticity formulation in dealing with the fluid dynamics with free surface flows. The project will be carried out for 3 years. The first year will concentrate the establishment of the models for two dimensional free surface flows. To verify the numerical model, the present study naturally gives more reasonable results on problems including the maximum run-up of a solitary wave reflected from the vertical and obliquity walls, the propagation of water waves over a block. In the second year, comparison between the 2D and 3D models for water waves over a block will be undertaken. In the third year, the density stratification of free surface flows and rotational effects will be modeled. The models will be calibrated and verified by using the laboratory or the field data. The development of these nonlinear free surface flow models will provide a predictive tool for the design guidance for practical engineers in the water pollutant control of the deteriorated environments of Taiwan coastal and river waters.application/pdf12847736 bytesapplication/pdfzh-TW國立臺灣大學土木工程學系暨研究所自由液面渦漩流場速度-渦度法有限元素法平行計算Free surfacesVortical flowsVelocity-Vorticity formulationFinite element methodsParallel computation[SDGs]SDG11reporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/2874/1/922611E002021.pdf