Numerical Studies of Bathymetry Effects on Waves Deformation Using Shallow Water Equations

• Main Authors: Wei-Chun Wu, 吳威均
• Other Authors: Shin-Jye Liang
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/18833303588802892081

碩士 === 國立臺灣海洋大學 === 海洋環境資訊學系 === 98 === A nonlinear shallow water model based on the depth-averaged, non-conservative shallow-water equations (SWE) is developed. The model uses least-squares finite-element method for space discretization, with method or space-time method for time integration. To study the accuracy and conservation property of space-time finite-element method, solitary wave solution of Equal Width (EW) equation is performed first. SWE model, where bottom slope is presented as a source term in the momentum equation which requires special treatment in other numerical method, is applied to bathymetry-wave interactions. Test cases include regular wave (1) in a constant depth channel, (2) in a slope channel, (3) past a submerged channel, and (4) past a channel with a step changing bottom, respectively. Case (1) - (3) uses method and case (4) uses space-time method for time integration. Computed results are compared with analytic solutions or available experiment data. Limitation of the model is also examined. Numerical results show that approximation of solitary waves of EW using Newton’s linearization is more accurate and better conserved than Zaki’s method (2000) is. However, the convergence radius of Newton’s method is more restrictive than that of Zaki’s method is. Generation of high-frequency waves is significant when nonlinear effect is important in wave-bathymetry interactions. Simulation of the model is not accurate for deep water waves (short waves), where dispersion effect plays an important role. In order to quantitatively investigate the deep water waves either the dispersive Boussinesq equations or non-hydrostatic pressure model is suggested for future study.