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International Conference on Developments in Marine CFD, 18 -19 November 2011, Chennai, India 2011: The Royal Institution of Naval Architects
 

Summary: International Conference on Developments in Marine CFD, 18 - 19 November 2011, Chennai, India
2011: The Royal Institution of Naval Architects
THE VARIATIONAL 2D BOUSSINESQ MODEL FOR WAVE PROPAGATION OVER A
SHOAL
D Adytia and E van Groesen, LabMath-Indonesia and University of Twente, The Netherlands
SUMMARY
The Variational Boussinesq Model (VBM) for waves [1] is based on the Hamiltonian structure of gravity surface waves.
In its approximation, the fluid potential in the kinetic energy is approximated by the sum of its value at the free surface
and a linear combination of vertical profiles with horizontal spatially dependent functions as coefficients. The vertical
profiles are chosen a priori and determine completely the dispersive property of the model. For coastal applications, the
1D version of the model has been implemented in Finite Element with piecewise linear basis functions and has been
compared with experiments from MARIN hydrodynamic laboratory for focusing wave group running above a flat
bottom [2] and for irregular waves running above a sloping bottom [3]. The 2D version of the model has been derived
and implemented using a pseudo-spectral method with a rectangular grid in [4,1]. A limitation of the later
implementation is a lack of flexibility when the model deals with a complicated domain such as a harbour. Here, we
will present an implementation of the model in 2D Finite Element which consistent with the derivation of the model via
the variational formulation. To illustrate the accuracy of wave refraction and diffraction over a complex bathymetry, the
experiment of Berkhoff et al, 1982 [5] is used to compare the FE results with measurements.
NOMENCLATURE
H Hamiltonian or total energy

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering