Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-01T02:23:20.180Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-dimensional modal method for shallow-water sloshing in rectangular basins

Published online by Cambridge University Press:  01 May 2012

M. Antuono ,
B. Bouscasse ,
A. Colagrossi  and
C. Lugni
M. Antuono*
Affiliation:
CNR-INSEAN, Via di Vallerano 139, 00128 Roma, Italy
B. Bouscasse
Affiliation:
CNR-INSEAN, Via di Vallerano 139, 00128 Roma, Italy
A. Colagrossi
Affiliation:
CNR-INSEAN, Via di Vallerano 139, 00128 Roma, Italy Centre of Excellence for Ship and Ocean Structures, NTNU, 7491 Trondheim, Norway
C. Lugni
Affiliation:
CNR-INSEAN, Via di Vallerano 139, 00128 Roma, Italy Centre of Excellence for Ship and Ocean Structures, NTNU, 7491 Trondheim, Norway
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A two-dimensional model for the analysis of sloshing phenomena in shallow-water conditions has been defined using Boussinesq-type depth-averaged equations. Thanks to a modal decomposition of the spatial field, the present model allows a straightforward and simple treatment of the exciting forces and can describe a generic motion. Comparisons with the experimental data available in the literature and with a smoothed particle hydrodynamics (SPH) scheme proved the proposed shallow-water model to be accurate, fast and robust.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 700 , 10 June 2012 , pp. 419 - 440
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Antuono, M., Colagrossi, A., Marrone, S. & Lugni, C. 2011 Propagation of gravity waves through SPH schemes with numerical diffusive terms. Comput. Phys. Commun. 182, 866–877.CrossRefGoogle Scholar
2. Antuono, M., Colagrossi, A., Marrone, S. & Molteni, D. 2010 Free-surface flows solved by means of SPH schemes with numerical diffusive terms. Comput. Phys. Commun. 181 (3), 532–549.CrossRefGoogle Scholar
3. Ardakani, H. A. & Bridges, T. J. 2011a Shallow-water sloshing in vessels undergoing prescribed rigid-motion in two dimensions. Eur. J. Mech. B/Fluids 31, 40–43.Google Scholar
4. Ardakani, H. A. & Bridges, T. J. 2011b Shallow-water sloshing in vessels undergoing prescribed rigid-motion in three dimensions. J. Fluid Mech. 667, 474–519.CrossRefGoogle Scholar
5. Bouscasse, B., Colagrossi, A., Colicchio, G. & Lugni, C. 2007 Numerical and experimental investigation of sloshing phenomena in conditions of low filling ratios. In 10th Numerical Towing Tank Symposium (NuTTS’07) Hamburg, Germany, 23–25 Sep. 2009. Curran Associates, Inc.Google Scholar
6. Bulian, G., Souto-Iglesias, A., Delorme, L. & Botia-Vera, E. 2010 Smoothed particle hydrodynamics (SPH) simulation of a tuned liquid damper. J. Hydraul. Res. 48 (1), 28–39.CrossRefGoogle Scholar
7. Colagrossi, A., Colicchio, G., Lugni, C. & Brocchini, M. 2010 A study of violent sloshing wave impacts using an improved SPH method. J. Hydraul. Res. 48, 94–104.CrossRefGoogle Scholar
8. Español, P. & Revenga, M. 2003 Smoothed dissipative particle dynamics. Phys. Rev. E 67, 026705-1:12.CrossRefGoogle ScholarPubMed
9. Faltinsen, O. M. 2005 Hydrodynamics of High-Speed Marine Vehicles. Cambridge University Press.Google Scholar
10. Faltinsen, O. M., Rognebakke, O. F., Lukovsky, I. A. & Timokha, A. N. 2000 Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. J. Fluid Mech. 407, 201–234.CrossRefGoogle Scholar
11. Faltinsen, O. M., Rognebakke, O. F. & Timokha, A. N. 2006 Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth. Phys. Fluids 18, 012103 1–14.CrossRefGoogle Scholar
12. Faltinsen, O. M. & Timokha, A. N. 2001 An adaptive multimodal approach to nonlinear sloshing in a rectangular tank. J. Fluid Mech. 432, 167–200.CrossRefGoogle Scholar
13. Faltinsen, O. M. & Timokha, A. N. 2002 Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth. J. Fluid Mech. 470, 319–357.CrossRefGoogle Scholar
14. Faltinsen, O. M. & Timokha, A. N. 2009 Sloshing. Cambridge University Press.Google Scholar
15. Gobbi, M. F., Kirby, J. T. & Wei, G. 2000 A fully nonlinear Boussinesq model for surface waves. Part 2. Extension to . J. Fluid Mech. 405, 181–210.CrossRefGoogle Scholar
16. Hill, D. F. 2003 Transient and steady-state amplitudes of forced waves in rectangular basins. Phys. Fluids 39 (6), 1576–1587.CrossRefGoogle Scholar
17. Keulegan, G. H. 1959 Energy dissipation in standing waves in rectangular basins. J. Fluid Mech. 6, 33–50.CrossRefGoogle Scholar
18. Lamb, H. 1945 Hydrodynamics. Cambridge University Press.Google Scholar
19. Landrini, M., Colagrossi, A., Greco, M. & Tulin, M. P. 2007 Gridless simulations of splashing processes and near-shore bore propagation. J. Fluid Mech. 591, 183–213.CrossRefGoogle Scholar
20. Lepelletier, T. G. & Raichlen, F. 1988 Nonlinear oscillations in rectangular tanks. J. Engng Maths 114 (1), 1–23.Google Scholar
21. Lighthill, J. 2001 Waves in Fluids. Cambridge University Press.Google Scholar
22. Lugni, C., Brocchini, M. & Faltinsen, O. M. 2006 Wave impact loads: the role of the flip-through. Phys. Fluids 18, 122101:1–17.CrossRefGoogle Scholar
23. Lugni, C., Brocchini, M. & Faltinsen, O. M. 2010a Evolution of the air cavity during a depressurized wave impact. II. The dynamic field. Phys. Fluids 22, 056102:1–13.Google Scholar
24. Lugni, C., Miozzi, M., Brocchini, M. & Faltinsen, O. M. 2010b Evolution of the air cavity during a depressurized wave impact. I. The kinematic flow field. Phys. Fluids 22, 056101:1–17.Google Scholar
25. Madsen, P. A., Bingham, H. B. & Liu, H. 2002 A new Boussinesq method for fully nonlinear waves from shallow to deep water. J. Fluid Mech. 462, 1–30.CrossRefGoogle Scholar
26. Madsen, P. A. & Shäffer, H. A. 2006 A discussion of artificial compressibility. Coast. Engng 53, 93–98.CrossRefGoogle Scholar
27. Marrone, S., Antuono, M., Colagrossi, A., Colicchio, G., Touzé, D. Le & Graziani, G. 2011 -SPH model for simulating violent impact flows. Comput. Meth. Appl. Mech. Engng 200, 1526–1542.CrossRefGoogle Scholar
28. Marrone, S., Colagrossi, A., Touzé, D. Le & Graziani, G. 2010 Fast free-surface detection and level-set definition in SPH solvers. J. Comput. Phys. 229, 3652–3663.CrossRefGoogle Scholar
29. Monaghan, J. J. 2005 Smoothed particle hydrodynamics. Rep. Prog. Phys. 68, 1703–1759.CrossRefGoogle Scholar
30. Nwogu, O. 1993 Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterways Port Coast. Ocean Engng 119, 618–638.CrossRefGoogle Scholar
31. Ockendon, H., Ockendon, J. R. & Johnson, A. D. 1986 Resonant sloshing in shallow water. J. Fluid Mech. 167, 465–479.CrossRefGoogle Scholar
32. Olsen, H. & Johnsen, K. 1975 Nonlinear sloshing in rectangular tanks: a pilot study on the applicability of analytical models. Tech. Rep. 74-72-5 Vol. 2. Det Norske Veritas (DNV), Hvik, Norway.Google Scholar
33. Pantazopoulos, M. 1987 Numerical solution of the general shallow water sloshing problem. PhD thesis, University of Washington, Seattle.Google Scholar
34. Randles, P. W. & Libersky, L. D. 1996 Smoothed particle hydrodynamics: Some recent improvements and applications. Comput. Meth. Appl. Mech. Engng 139, 375–408.CrossRefGoogle Scholar
35. Souto-Iglesias, A., Delorme, L., Pérez-Rojas, L. P. & Abril-Pérez, S. 2006 Liquid moment amplitude assessment in sloshing type problems with smooth particle hydrodynamics. Ocean Engng 33 (11), 1462–1484.CrossRefGoogle Scholar
36. Veeramony, J. & Svendsen, I. A. 2000 The flow in surf-zone waves. Coast. Engng 39, 93–122.CrossRefGoogle Scholar
37. Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley & Sons.Google Scholar