Two-Dimensional Velocity-Vorticity Formulation For Incompressible Flows with Free Surfaces By The Finite Element Method

• Main Authors: Der-Chang Lo, 羅德章
• Other Authors: Der-Liang Young
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/94140273877786687504

碩士 === 國立臺灣大學 === 土木工程學研究所 === 88 === In this study, the motion of incompressible flows with free surfaces are solved by the finite element method using the velocity-vorticity formulation. To demonstrate the model feasibility, first of all the steady Stokes flow in a square cavity and circular cavity are computed. The results of square cavity flow are comparable with the numerical solutions of Burggraff (1966, FDM) and Yang (1997, BEM). In the meantime, the results of circular cavity flow are also compared to the exact solution solved by Hwu et al. (1997). Then the unsteady Navier-Stokes flow are computed and compared with other models, The results of this study show that the numerical method is quite accurate and successful. In the free-surface part, the interior flow equations are basically treated by the finite element, while the boundaries conditions are solved by using the appropriate finite difference schemes. The arbitrary Lagrangin-Eulerian method is adopted so that the irregular computational domain can be easily discretized and the moving boundaries can be coped with by a moving mesh technique. To verify the numerical model, the present study naturally gives more reasonable results on problems including the solitary wave viscous damping, interactions between solitary wave, the maximum run-up of a solitary wave reflected from a vertical wall, the seiche phenomenon in a rectangular reservoir. These applications reveal that finite element and finite difference analysis are very powerful approach in the realm of computational fluid mechanics.