SIMULATION OF VARIOUS SHALLOW WATER WAVE PROBLEMS USING THE MAC-CORMACK METHOD
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 approx...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/63866 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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