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orce ment for incompr essible flows [15,1 7] ch aracterize the numeri cal formu lations and approxim ations. Bes ides, severa l ano ther issue s such as the coupling betw een solid an d fluid have bee n also intens ivel y studied for the reliable numerical simulat ion.

The mesh dist ortion and the mesh ad aptation are strong ly related to the choice of kinema tic de scription approach (e.g. Lagrangi an, Euleri an, or ALE (arbi trary Lag rangia n–Euleri an) [9]). Currentl y, this problem can be resol ved, to a large extent , by emp loying the ALE method with the help of a suitable remes hing and smoot hing algori thm [18] . Regar ding this matter, the reader may refer to [4,9,12,1 3,16,17] for more de tailed discus sion. On the other hand, the fluid flow has been tradi tionally form ulated by eithe r the potential flow theory [5,8,11, 14,19] or the full Navi er–Stoke s equa tions. In the form er case, the free surface co nfigurati on is tracke d by time-i ntegra ting the nonl inear kinema tic and dynami c condition s, and the flow velocity and the dy namic pressur e are usu ally interpo lated from the veloci ty potenti al appro ximated. Ho wever, in the latter case in whi ch both flow veloci ty an d dynami c pressur e are the prim ary state varia bles, the flow bounda ry identificati on varie s to the choice of kinema tic de scription appro ach. Referrin g to the papers by Soulaim ani and Saad [20] and Cho a nd Lee [4], the bounda ry tracki ng in both Lag rangia n and AL E ap-proaches is straight forward because fluid mesh mo ves exactl y with fluid particles . But , in the Euleri an approach the bounda ry tracki ng requ ires any special charact eristic (volum e fract ion) functio n [21] wi th the mesh refin ement along the flow bounda ry.

References
[1] J.R. Cho, J.M. Song, J.K. Lee, Finite element techniques for the free-vibration and seismic analysis of liquid-storage tanks, Finite Elem. Anal. Des. 37 (2001) 467–483.
[2] A.M. Silvera, D.G. Stephens, H.W. Leonard, An experimental investigation of liquid oscillations in tanks with various baffles, https://www.51lunwen.org/englishpaper/ NASA Technical Note D-715, 1961.
[3] D.G. Stephens, Flexible baffles for slosh damping, J. Spacecraft Rockets 3 (5) (1966) 765–766.
[4] J.R. Cho, S.Y. Lee, Dynamic analysis of baffled fuel-storage tanks using the ALE finite element method, Int. J. Numer. Methods Fluids 41 (2003) 185–208.
[5] J.R. Cho, H.W. Lee, K.W. Kim, Free vibration analysis of baffled liquid-storage tanks by the structural-acoustic finite element formulation, J. Sound Vibr. 258 (5) (2003) 847–866.
[6] G.W. Housner, Dynamic pressures on accelerated fluid containers, Bull. Seismol. Soc. Am. 47 (1957) 15–35.
[7] S. Silverman, H.N. Abramson, Lateral sloshing in moving containers, NASA SP-106, 1966, pp. 13–78.
[8] M. Ikegawa, Finite element analysis of fluid motion in a container, Finite Elem. Methods Flow Prob. (1974) 737–738.
[9] C.W. Hirt, A.A. Amsden, J.L. Cook, An arbitrary Lagrangian Eulerian computing method for all flow speeds, J. Comput. Phys. 14 (1974) 227–253.