MATHEMATICAL MODEL STUDY OF WAVE RUNUP BASED ON BOUSSINESQ EQUATION

• Main Author: CHRYSANTI (NIM : 25016055), ASRINI
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/25867
• Institution: Institut Teknologi Bandung

<p align="justify">Numerical modeling requires a governing equation that capable of modeling events on the shore. The accuracy of the numerical model is determined from the compatibility of the mathematical equation used to describe the process occurring in the flow. The most common equation used to simulate water flow is the Saint Venant equation based on the assumption of the hydrostatic pressure <br /> <br /> <br /> <br /> distribution in the vertical direction. However, for certain flow behaviors, which, as in the case of transition flows where there is a shock, these assumptions should not be justified and need to be added the dispersion terms which take into account the non-hydrostatic pressure distribution conditions. The numerical model based on the Boussinesq equation represents a practical and accurate choice for the <br /> <br /> <br /> <br /> simulation of the hydrodynamic process near the shore. The solution of the Boussinesq equation with several schemes has been done in one of the previous studies by completing the classical Boussinesq equation with the Maccormack scheme, and with the fourth order scheme (central scheme). Both models are still not perfect in modeling wave propagation especially when wave breaks. In this study, we tried to modify the model that was developed on previous study by replacing the governing equation by Madsen (1992) and adding QUICK schemes <br /> <br /> <br /> <br /> for convection term. It is expected that by doing this modification, the numerical results become more accurate and the model can be applied to case studies. In Indonesia, tidal floods often occur in coastal cities such as northern Jakarta and Semarang. Tidal flood modeling needs to consider tidal and wave patterns <br /> <br /> <br /> <br /> so it will be difficult to model in a one dimensional model. However, for propagation of tidal flood simulation can be done with one-dimensional model, <br /> <br /> <br /> <br /> where the direction of the wave in the shallow sea is perpendicular to the beach so that the analysis of one dimension is sufficient to analyze the propagation. <br /> <br /> <br /> <br /> The tidal height used is the highest tide at the time of the event and is considered a constant value in the modeling. From the analysis we found that one dimensional model can predict the propagation well especially for the steep slope, but not good enough for the sloping slopes. Simulation also applied in Ciliwung river estuary, the results show in good agreement with the data.<p align="justify">