ALE and Fluid Structure Interaction for Sloshing Analysis


  • Z Ozdemir
  • M Moatamedi
  • Y Fahjan
  • M Souli



Liquid containment tanks are, generally, subjected to large deformations under severe earthquake conditions due to coupling forces between tank and the contained liquid. The accurate description of these forces is vital in order to diminish or eliminate the potential risk of tank failure during an earthquake. Yet, analytical formulations derived for the seismic analysis of liquid storage tanks are not capable to capture the complex fluid-structure effects since they include many assumptions and simplifications not only for the behavior of fluid and structure but also for the external excitation. On the other hand, an appropriate numerical method allows us to cope with large displacements of free surface of the fluid, high deformations of the structure and correctly predicts the hydrodynamic forces due to the high-speed impacts of sloshing liquid on a tank wall and roof. For this purpose, a new coupling algorithm based on the penalty formulation of finite element method which computes the coupling forces at the fluidstructure interface is developed in this paper. This algorithm is constructed on a two superimposed mesh systems which are a fixed or moving ALE mesh for fluid and a deformable Lagrangian mesh for structure. The fluid is represented by Navier-Stokes equations and coupled system is solved using an explicit time integration scheme. In order to verify the analysis capability of coupling algorithm for tank problems, numerical method is applied for the analyses of a rigid rectangular tank under harmonic excitation and a flexible cylindrical tank subjected to earthquake motion and numerical results are compared with existing analytical and experimental results. Strong correlation between reference solution and numerical results is obtained in terms of sloshing wave height.


L.S. Jacobsen, 1949, Impulsive hydrodynamics of fluid inside a cylindrical tank and of fluid surrounding a cylindrical pier. Bulletin of the Seismological Society of America, 39, 3, 189-204, July.

G.W. Housner, 1954, Earthquake pressures on fluid containers. 8th Technical Report under Office of Naval Research, California Institute of Technology, Pasadena, California, August.

G.W. Housner, Dynamic pressures on accelerated fluid containers. Bulletin of the Seismological Society of America, 47, 1, 15-35, January, 1957.

G.W. Housner, The dynamic behavior of water tanks. Bulletin of the Seismological Society of America, 53, 2, 381-387, February, 1963.

A.S. Veletsos, J.Y. Yang, Earthquake response of liquid storage tanks. Advances in Civil Engineering Through Engineering Mechanics, Proceedings of the Engineering Mechanics Division Specialty Conferences, ASCE, Raleigh, North Carolina, 1-24, 1977.

Haroun M. A. and Housner, G. W., 1981a, “Seismic Design of Liquid Storage Tanks”, Journal of the Technical Councils of ASCE, Vol. 107, No. TC1, April.

Haroun MA and Housner GW, 1981b, “Earthquake response of deformable liquid storage tanks”. Journal of Applied Mechanics, ASME, Vol. 48, pp. 411-418., June.

Veletsos A.S., 1984, “Seismic Response and Design of Liquid Storage Tanks, in Guidelines for the Seismic Design of Oil and Gas Pipeline Systems”, ASCE, p. 255-370, 443-460.

Faltinsen, O.M., “A numerical nonlinear method of sloshing in tanks with two-dimensional flow”, J. Ship Res. 22 (1978) 193-202.

F.D. Fischera, and F.G. Rammerstorferb, 1999, “A Refined Analysis of Sloshing Effects in Seismically Excited Tanks”, International Journal of Pressure Vessels and Piping, Vol. 76, pp. 693-709.

Malhotra, P. K. and A. S. Veletsos, 1994a, “Beam Model for Base-Uplifting Analysis of Cylindrical Tanks”, Journal of Structural Engineering, ASCE, Vol. 120, No. 12, pp. 3471-3488, December.

Malhotra, P. K. and A. S. Veletsos, 1994b, “Uplifting Analysis of Base Plates in Cylindrical Tanks”, Journal of Structural Engineering, ASCE, Vol. 120, No. 12, pp. 3489-3505, December.

Malhotra, P. K. and A. S. Veletsos, 1994c, “Uplifting Response of Unanchored Liquid-Storage Tanks”, Journal of Structural Engineering, ASCE, Vol. 120, No. 12, pp. 3525-3547, December.

Malhotra, P. K., 1995, “Base Uplifting Analysis of Flexibly Supported Liquid-Storage Tanks”, Earthquake Engineering and Structural Dynamics, Vol. 24, Issue 12, pp. 1591-1607.

El-Zeiny, A., 1995, “Nonlinear Time-Dependent Seismic Response of Unanchored Liquid Storage Tanks”, PhD Dissertation, Department of Civil and Environmental Engineering, University of California, Irvine.

Barton DC and Parker JV., 1987, “Finite element analysis of the seismic response of anchored and unanchored liquid storage tanks”, Earthquake Engineering and Structural Dynamics;15(3):299-322.

Souli, M., Ouahsine, A. and Lewin, L., “ALE formulation for fluid-structure interaction problems”, Computer Methods in Applied Mech. and Eng. 190 (2000) 659-675.

Souli, M and Zolesio, J P. Arbitrary Lagrangian-Eulerian and free surface methods in fluids mechanics, Computational Methods In Applied Mechanics and Engineering, 2001 191 451-466.

Aquelet, N., Souli, M., and Olovson L., “Euler Lagrange coupling with damping effects: Application to slamming problems”, Computer Methods in Applied Mechanics and Engineering, Vol. 195 , pp 110-132, (2005).

Chen, Y. H., Hwang, W. S. and Ko, C. H., 2007, “Sloshing Behaviours of Rectangular and Cylindrical Liquid Tanks Subjected to Harmonic and Seismic Excitations”, Earthquake Engineering and Structural Dynamics, Vol. 36, pp.1701-1717.

Liu, D. and Lin, P., “A numerical study of three-dimensional liquid sloshing in tanks”, Journal of Computational Physics, 227 (2008), 3921-3939.

Mitra, S., Upadhyay, P. P., and Sinhamahapatra, K. P., 2008, “Slosh Dynamics of Inviscid Fluids in Two-Dimensional Tanks of Various Geometry Using Finite Element Method”, International Journal for Numerical Methods in Fluids, Vol. 56, pp.1625-1651.

M. S. Razzaghi and S. Eshghi, 2004, “Behavior of Steel Oil Tanks due to Near-Fault Ground Motion”, 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August 1-6.

Kana, D. D., 1979, “Seismic Response of Flexible Cylindrical Liquid Storage Tanks”, Nuclear Engineering and Design, Vol. 52, pp. 185-199.

Clough, D. P., 1977, Experimental evaluation of seismic design methods for broad cylindrical tanks, UCB/EERC-77/10, PB-272 280.

Manos and Clough, 1982, “Further study of the earthquake response of a broad cylindrical liquidstorage tank model” UCB/EERC-82/07, Earthquake Engineering Research Center, University of California, Berkeley, EERC-82/07.

Manos, G. C., 1986, “Dynamic response of a broad storage tank model under a variety of simulated earthquake motions.” Proc. ∼ 3rd U.S. Nat. Conf. on Earthquake Engrg., Earthquake Engineering Research Institute, E1 Cerrito, Calif., 2131-2142.

Tanaka, Motoaki, Sakurai, Ishida, Tazuke, Akiyama, Kobayashi and Chiba, 2000, “Proving Test of Analysis Method on Nonlinear Response of Cylindrical Storage Tank Under Severe Earthquakes”, Proceedings of 12th World Conference on Earthquake Engineering (12 WCEE), Auckland, New Zealand.

T. Belytschko, W.K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons, New York, 2000.

D.J. Benson, Amixture theory for contact in multi-material eulerian formulations, Comput. Meth. Appl. Mech. Eng. 140 (1997) 59-86.

T.J.R. Hughes, W.K. Liu and T.K. Zimmerman, “Lagrangian Eulerian finite element formulation for viscous flows”, J. Computer Methods Applied Mechanics and Engineering, 29 (1981) 329-349.

Benson, D.J., “Computational Methods in Lagrangian and Eulerian Hydrocodes”, Computer Methods in Applied Mech. and Eng. 99 (1992) 235-394.

Flanagan, D.P. and Belytschko, T., “A Uniform Strain Hexahedron and Quadrilateral and Orthogonal Hourglass Control”, Int. J. Numer. Meths, Eng. 17,679-706 (1981).

Richtmyer, R.D. and Morton, K.W. (1967), Difference Equations for Initial-Value Problems, Interscience Publishers, New York.

Young, D.L., “Time-dependent multi-material flow with large fluid distortion”, Numerical Methods for Fluids Dynamics, Ed. K. W. Morton and M.J. Baines, Academic Press, New-York (1982).

Alia, A. and Souli M., 2006, “High explosive simulation using multi-material formulations”, Applied Thermal Engineering, Vol. 26, pp.1032-1042.

Woodward, P.R., and Collela, P., “The numerical simulation of two-dimensional fluid flow with strong shocks”, Lawrence Livermore National Laboratory, UCRL-86952, (1982).

Van Leer, B., “Towards the Ultimate Conservative Difference Scheme. IV. A New Approach to Numerical Convection”, Journal of Computational Physics 23 (1977) p 276-299.

S. Rabier, M. Medale, Computation of free surface flows with a projection FEM in a moving mesh framework, Comput. Methods Appl. Mech. Engrg. 192 (41-42) (2003) 4703-4721.

D.J. Benson, An efficient, accurate, simple ALE method for nonlinear finite element programs, Comput. Methods Appl. Mech. Engrg. 72 (1989) 305-350.

Z.H. Zhong, Finite Element Procedures for Contact-impact Problems, Oxford University Press, Oxford, 1993.

T. Belytschko, M.O. Neal, Contact-impact by the pinball algorithm with penalty, projection, and Lagrangian methods, in: Proceedings of the Symposium on Computational Techniques for Impact, Penetration, and Performation of Solids AMD, vol. 103, ASME, New York, NY, 1989, pp. 97-140.



How to Cite

Ozdemir, Z., Moatamedi, M., Fahjan, Y. and Souli, M. (2009) “ALE and Fluid Structure Interaction for Sloshing Analysis”, The International Journal of Multiphysics, 3(3), pp. 307-336. doi: 10.1260/175095409788922257.




Most read articles by the same author(s)

1 2 3 > >>