THE PNC1- P1 FINITE ELEMENT METHOD FOR SIMULATION USING SHALLOW WATER EQUATION

• Main Author: Veri Swastika, Putu
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/47745
• Institution: Institut Teknologi Bandung

This thesis deals with the linear shallow water equations for one- and twodimensional cases. The equations are expressed in terms of surface elevation and potential velocity variables. The weighted Galerkin residual method is implemented to get a weak formulation of the shallow water equations. Next, the approximate solution can be obtained from the weak form, by adopting the ???????? ???????? ? ???????? basis function pairs which are used simultaneously. The continuous hat function, denoted as ????????, is used as a basis function for the surface elevation. While the discontinuous function, denoted as ???????? ????????, is used as a basis function for the velocity potential. The use of these two basis functions alternately will result in the formation of a multilevel grid. Then several numerical simulations were performed. First, validation using the analytic solution of standing wave simulation shows that the proposed method has good accuracy. Second, the simulation results of the shoaling phenomena show a good agreement with the analytical WKB formula. The third simulation is about wave propagation due to a submerged breakwater. The result shows good agreement with the analytical formula, and the optimal dimension of the breakwater is confirmed. The advantage of this numerical method is that it is free of damping, moreover it admits mass and energy conservation. Subsequently, the analogous method is extended to the two-dimensional shallow water equations, and several simulations were carried out successfully.