Assessment of an Advanced Finite Element Tool For the Simulation of Fully-nonlinear Gravity Water Waves

The aim of the present study is to provide a rigorous analysis of the water wave modelling capabilities of the advanced multipurpose CFD code Fluidity. This code has been developed at Imperial College London over a large number of years and benefits from an open source GNU license. In contrast to similar studies adopting closed-source in-house or commercial solutions, the results presented herein may be verified by any computer literate reader. The investigation focuses on the simulation of gravity water waves; their detailed understanding being fundamental to the design of many offshore (marine) solutions, including the emerging fields of wave energy conversion and floating offshore wind applications. Both small amplitude (linear hydrodynamics) and finite amplitude (nonlinear hydrodynamics) regular waves are simulated in a 2D Numerical Wave Tank (NWT). First, and assessment of the NWT’s capabilities in accurately modelling wave propagation and wave energy conservation of linear waves is undertaken. Subsequently, the simulated wave field is directly compared with results obtained from linear wavemaker theory. For the purpose of the nonlinear wave investigation, two wave generation techniques are adopted, and comparisons with a high-order potential flow theory are made. The overall agreement between the simulation results and theory was found to be very good.

[1]  Johannes Spinneken,et al.  Second-order wave maker theory using force-feedback control. Part I: A new theory for regular wave generation , 2009 .

[2]  M Kashiwagi.  Non-linear simulations of wave-induced motions of a floating body by means of the mixed Eulerian-Lagrangian method , 2000 .

[3]  C. C. Pain,et al.  A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling , 2008, 0805.4380.

[4]  Christopher C. Pain,et al.  Coupled FEMDEM/Fluids for coastal engineers with special reference to armour stability and breakage , 2009 .

[5]  J. N. Newman.  Analysis of wave generators and absorbers in basins , 2010 .

[6]  Alain H. Clément,et al.  Recent Research And Development of Numerical Wave Tank - A Review , 1999 .

[7]  Marcel Zijlema,et al.  An accurate and efficient finite‐difference algorithm for non‐hydrostatic free‐surface flow with application to wave propagation , 2003 .

[8]  Hemming A. Schäffer,et al.  SECOND-ORDER WAVEMAKER THEORY FOR IRREGULAR WAVES , 1996 .

[9]  Stephan T. Grilli,et al.  Numerical Generation and Absorption of Fully Nonlinear Periodic Waves , 1997 .

[10]  J. J. Leendertse,et al.  Aspects of a computational model for long-period water-wave propagation , 1967 .

[11]  John D. Fenton,et al.  A Fifth‐Order Stokes Theory for Steady Waves , 1985 .

[12]  Meir Pilch.  Laboratory Wave-Generating Apparatus , 1953 .

[13]  John M. Niedzwecki,et al.  Fully Nonlinear Multidirectional Waves by a 3-D Viscous Numerical Wave Tank , 2001 .

[14]  David Ingram,et al.  On geometric design considerations and control methodologies for absorbing wavemakers , 2011 .

[15]  Tim Bunnik,et al.  Validation of Wave Propagation in Numerical Wave Tanks , 2005 .

[16]  C. H. Hague,et al.  A multiple flux boundary element method applied to the description of surface water waves , 2009, J. Comput. Phys..