Simulation of 2-D nonlinear waves using finite element method with cubic spline approximation

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractThis is the first paper to present a hybrid method coupling a Improved Meshless Local Petrov Galerkin method with Rankine source solution (IMLPG_R) based on the Navier Stokes (NS) equations, with a finite element method (FEM) based on the fully nonlinear potential flow theory (FNPT) in order to efficiently simulate the violent waves and their interaction with marine structures. The two models are strongly coupled in space and time domains using a moving overlapping zone, wherein the information from both the solvers is exchanged. In the time domain, the Runge-Kutta 2 nd order method is nested with a predictor-corrector scheme. In the space domain, numerical techniques including 'Feeding Particles' and two-layer particle interpolation with relaxation coefficients are introduced to achieve the robust coupling of the two models. The properties and behaviours of the new hybrid model are tested by modelling a regular wave, solitary wave and Cnoidal wave including breaking and overtopping. It is validated by comparing the results of the method with analytical solutions, results from other methods and experimental data. The paper demonstrates that the method can produce satisfactory results but uses much less computational time compared with a method based on the full NS model.

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“…The procedure has been described in our previous publications (e.g., [10,47,48]) but is summarized below for completeness.…”

Section: Fully Nonlinear Potential Theory and Finite Element Methods (mentioning

confidence: 99%

A hybrid method for modelling two dimensional non-breaking and breaking waves

Sriram

Schlurmann

2014

Journal of Computational Physics

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“…As the gauges are usually not used in such small water depths they were thoroughly calibrated prior to the experiments and additionally a very well validated numerical model (e.g. Sriram et al, 2006;Sriram et al, 2007) based on fully non-linear potential flow theory (FNPT) has been applied to verify the measurements and vice versa. As the wave heights are critically small it is further essential for an accurate generation of these long period waves with a piston type wave maker that there is no water leakage at the edges of the wave board (e.g.…”

Section: Experimental Set-upmentioning

confidence: 99%

On the Generation of Tsunami in a Large Scale Wave Flume

Schimmels

Sriram²,

Didenkulova

et al. 2014

Int. Conf. Coastal. Eng.

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“…In order to analyze the transformation of long waves during propagation in shallow water depths a numerical wave tank based on fully nonlinear potential flow theory (Sriram et al 2006) and KdV equations (Sergeeva et al 2011) is used. In both models the fluid is assumed to be incompressible, the flow is irrotational and viscous forces are neglected.…”

Section: Numerical Modellingmentioning

confidence: 99%