SIMULATION OF VARIOUS SHALLOW WATER WAVE PROBLEMS USING THE MAC-CORMACK METHOD

• Main Author: Eriswandi, Venita
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/63866
• Institution: Institut Teknologi Bandung

The Shallow Water Equation (SWE) is an equation that is often used for modeling waves in shallow water areas. The SWE equation is a hyperbolic nonlinear system of differential equations; which consists of the equation conservation of mass and momentum balance. In this thesis, the numerical approximation of the SWE equation is discussed, namely the MacCormack method. The MacCormack method is a finite difference scheme consisting of two steps, the predictor and the corrector. This scheme is conditionally stable with a dispersion type numerical error; these aspects are discussed here. Furthermore, the MacCormack scheme is used to simulate several wave phenomena, such as the d’Alembert phenomenon, wave shoaling, standing wave and dam break. Simulations are carried out with linear and nonlinear SWE equations, depending on the case. From the simulation results and comparisons with analytical formulas, it can be concluded that the MacCormack scheme is suitable for SWE, and can provide accurate results on the d’Alembert phenomenon, wave shoaling and standing wave. While the MacCormack scheme has not been able to accurately simulate the dam break phenomenon, but it can simulate the shock wave phenomenon well.