A HIGH-ORDER SPECTRAL ELEMENT UNIFIED BOUSSINESQ MODEL FOR FLOATING POINT ABSORBERS
AbstractNonlinear wave-body problems are important in renewable energy, especially in case of wave energy converters operating in the near-shore region. In this paper we simulate nonlinear interaction between waves and truncated bodies using an efficient spectral/hp element depth-integrated unified Boussinesq model. The unified Boussinesq model treats also the fluid below the body in a depth-integrated approach. We illustrate the versatility of the model by predicting the reflection and transmission of solitary waves passing truncated bodies. We also use the model to simulate the motion of a latched heaving box. In both cases the unified Boussinesq model show acceptable agreement with CFD results - if applied within the underlying assumptions of dispersion and nonlinearity - but with a significant reduction in computational effort.
C. Eskilsson, J. Palm, J. P. Kofoed, and E. Friis-Madsen. Cfd study of the overtopping discharge of the wave dragon wave energy converter. Renewable Energies Offshore, pages 287-294, 2015b.
G. Giorgi and J. V. Ringwood. Implementation of latching control in a numerical wave tank with regular waves. Journal of Ocean Engineering and Marine Energy, 2(2):211-226, 2016.
D. Greaves and G. Iglesias, editors. Wave and Tidal Energy. Wiley, 2018.
J. S. Hesthaven and T. Warburton. Nodal discontinuous Galerkin methods: algorithms, analysis, and applications. Springer Science & Business Media, 2007.
T. Jiang. Ship Waves in Shallow Water. Fortschritt-Berichte VDI. Reihe 12, Verkehrstechnik /Fahrzeugtechnik. VDI-Verlag, 2001. ISBN 9783183466122.
G. Karniadakis and S. Sherwin. Spectral/hp element methods for computational fluid dynamics. Oxford University Press, 2013.
J.-W. Kim, H. Jang, A. Baquet, J. O'Sullivan, S. Lee, B. Kim, A. Read, and H. Jasak. Technical and economical readiness review of CFD-based numerical wave tank for offshore floater design. In Proceedings of Offshore Technology Conference, Houston, 2016.
D. Lannes. On the dynamics of floating structures. Annals of PDE, 3(1):11, 2017a.
D. Lannes. Personal communication, 2017b.
P. Lin. A multiple-layer s-coordinate model for simulation of wave-structure interaction. Computers & fluids, 35(2):147-167, 2006.
P. A. Madsen and H. A. Schäffer. A review of boussinesq-type equations for surface gravity waves. In Advances in coastal and ocean engineering, pages 1-94. World Scientific, 1999.
P. A. Madsen and O. R. Sørensen. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry. Coastal Engineering, 18(3-4):183-204, Dec. 1992. ISSN 03783839. doi: 10.1016/0378-3839(92)90019-q.
J. Nørgaard and T. Andersen. Investigation of wave transmission from a floating wave dragon wave energy converter. In Proceedings of the 22nd International Offhore and Polar Engineering Conference, Rhodes, 2012.
J. Palm, C. Eskilsson, G. M. Paredes, and L. Bergdahl. Cfd simulation of a moored floating wave energy converter. In Proceedings of the 10th European Wave and Tidal Energy Conference, Aalborg, Denmark, volume 25, 2013.
J. Palm, C. Eskilsson, G. M. Paredes, and L. Bergdahl. Coupled mooring analysis of floating wave energy converters using CFD: formulation and validation. International Journal of Marine Energy,, pages 83- 99, 2016.
D. H. Peregrine. Long waves on a beach. Journal of fluid mechanics, 27(4):815-827, 1967.
E. Ransley, D. Greaves, A. Raby, D. Simmonds, M. Jakobsen, and M. Kramer. Rans-vof modelling of the wavestar point absorber. Renewable Energy, 109:49-65, 2017.
M. Ricchiuto and A. G. Filippini. Upwind residual discretization of enhanced boussinesq equations for wave propagation over complex bathymetries. Journal of Computational Physics, 271:306-341, 2014.
Y. Yu and Y. Li. Reynolds-averaged navier-stokes simulation of the heave performance of a two-body floating-point absorber wave energy system. Computers & Fluids, 73:104-114, 2013.