2006 Volume 71 Issue 609 Pages 89-96
This paper proposes a finite element method for nonlinear sloshing analysis of perfect fluids. In this paper, the discrete governing equations of free surface flows are derived based on the variational principle. The energy functional is denoted by the volume integration of the Bernoulli's pressure equation, and by descritizing this functional previously, i.e. by applying the Ritz method, the governing equations are easily obtained. Furthermore, we introduce the scheme that the governing equations contain the movement rules of the fluid element nodes in which the elements automatically change shape along with the free surface deformation. Also, the several time-marching schemes for the governing equations are examined. On one of their schemes, we find that the sloshing behaviors are expressed as the dynamic equation of a nonlinear spring-mass-damper system, where the mass depends on the displacement of the spring. The results are compared with the ealier works on the numerical examples, and the effectiveness of the proposed method is confirmed.
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