Abstract
This paper shows some 2DV examples of recent advances related to the long-term, ongoing development of an elaborate, fully dispersive and highly nonlinear 3D phase resolving wave model based on the convolution-type approach. Using impulse response functions pre-computed by solving local Laplace problems the model is entirely explicit in space during the evolution in time. The explicit convolution integral involves only the near field surface variables and eliminates the need for solving global systems of equations. The first example is a linear random-wave application to wavemaker performance in a flume with a cavity behind an elevated generator and illustrates the capability of the model to handle complex geometry. The second example demonstrates the ability to generate and propagate highly nonlinear regular waves starting with transients entering still water. The third example concerns highly nonlinear regular deep-water waves and shows how the surface variables can be post-processed to provide the internal wave kinematics throughout the water column all the way to the free surface.References
Bateman W.J.D., Swan C., Taylor P.H., 2003. On the calculation of the water particle kinematics arising in a directionally spread wavefield, J. of Computational Physics,186, 70-92
Bingham, H.B., Agnon, Y., 2005. A Fourier-Boussinesq method for nonlinear water waves. Eur. J. Mech B/Fluids, 24, 255-274.
Dommermuth, D.G., Yue, D.K.Y., 1987. A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267-288.
Madsen, P.A., Bingham, H.B., Schäffer, H.A., 2003. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis. Proc. R. Soc. Lond. A459, 1075-1104.
Madsen, P.A., Agnon, Y., 2003. Accuracy and convergence of velocity formulations for water waves in the framework of Boussinesq theory. J. Fluid Mech. 477,. 285-319.
Rienecker, M.M., Fenton, J.D., 1981. A Fourier approximation method for steady water waves. J. Fluid Mech. 104, 119-137.
Schäffer, H.A., 2004. Accurate determination of internal kinematic from numerical wave model results. Coastal Engineering 50, 199-211.
Schäffer, H.A., 2008. Comparison of Dirichlet-Neumann operator expansions for nonlinear surface gravity waves. Coastal Engineering 55, 288-294.
Schäffer, H.A., 2009. A fast convolution approach to the transformation of surface gravity waves: Linear waves in 1DH. Coastal Engineering 56, pp 513-533
Schäffer, H.A., 2012. Towards wave disturbance in ports computed by a deterministic convolution-type model. Proceedings of 33rd International Conference on Coastal Engineering, ASCE.
West, B.J., Brueckner, K.A., Janda, R.S., Milder D.M., Milton, R.L., 1987. A new numerical method for surface hydrodynamics. J. Geophys. Res. 92(C11), 11803-11824.