Exploring the (boundaries) of the Moving Boundary Problem
C.O. Hermans (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Henk Schuttelaars – Mentor (TU Delft - Mathematical Physics)
Chris Kleijn – Mentor (TU Delft - ChemE/Transport Phenomena)
Carolina Urzúa-Torres – Graduation committee member (TU Delft - Numerical Analysis)
Bijoy Bera – Graduation committee member (TU Delft - ChemE/Transport Phenomena)
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Abstract
The sea and the shoreline form a complex ecosystem driven by tides. So far, studies often ignore the moving boundary caused by these tides. The focus of this thesis to incorporate this boundary by using a coordinate transformation and a time-explicit numerical method. To achieve this, first the one-dimensional shallow water equations are derived from the 3D Navier Stokes equations. Then these 1D equations are non-dimensionalized and the coordinate transformation is done. This results in a system of non-linear equations. The seabed is modelled as a straight line. At the seaward side there is a periodic forced wave and at the landward side the water depth is 0. The time-explicit numerical method of Lax-Friedrichs is used. This method is stable under a more restricted Courant-Friedrichs-Lewy condition and is convergent for refined grids. For the Ameland inlet system the water depth, velocity and length of the basin results are calculated and compared to a simplified model and complemented by a Fourier analysis. The results are realistic (constant in the beginning of the basin with visible non-linearities at the landward side). An analysis is done to understand how the model behaves for dierent physical parameters, such as: the amplitude of the periodically forced wave, the undisturbed water depth, the length of the basin and the resistance. The model remains stable and the results are realistic.