Time-accurate stabilized finite element model for nonlinear shallow-water waves

Introduction of a time-accurate stabilized finite element approximation for the numerical investigation of fully/weakly nonlinear and weakly dispersive shallow-water waves is presented in this dissertation. To make the time approximation match the order of accuracy of the spatial representation of the linear triangular elements by the Galerkin finite element method, the high accuracy time integration of the implicit multistage Pade method is used for the development of the numerical scheme. The Streamline-Upwind Petrov-Galerkin (SUPG) method with cross-wind diffusion is employed to stabilize the scheme and suppress the spurious oscillations, usually common in the numerical computation of convection-dominated flow problems. The performance of numerical stabilization and accuracy is addressed. Treatments of various boundary conditions, including the open boundary conditions, the solid wall boundary conditions along boundaries with irregular geometry, are also described.; The performance of the present numerical models is demonstrated by various case studies, including free travel of solitary waves in a rectangular channel, wave-wave interaction of solitary waves, solitary wave interaction with a single cylinder and an array of four cylinders, and solitary wave propagation over a semicircular shoal. Numerical results showing the comparisons with analytical solutions, experimental measurements and other published numerical results are presented and discussed.; For the study of wave and porous structure interaction, theoretical investigations on solitary waves encountering a surface-piercing concentric porous cylinder system are conducted. The outer cylinder is porous and considered thin in thickness, while the inner cylinder is solid. Both cylinders are rigidly fixed on the bottom. Following Isaacson's (1983) approach, the solutions were obtained for free-surface elevation and the corresponding velocity potential in terms of Fourier integrals. Numerical results are presented to show the effects of incident wave condition, porosity of the outer cylinder and radius ratio on wave forces and wave elevations around the inner and outer cylinders.