Absolute nodal coordinate finite element approach to the two-dimensional liquid sloshing problems

Abstract

Two-dimensional large-amplitude liquid sloshing in the rectangular rigid container is numerically simulated through absolute nodal coordinate finite element method, which can describe the large deformation of continuum by using a small number of elements. The incompressible constraint of Newtonian fluid is imposed by the penalty function method. Furthermore, the motion of rigid container is described by absolute nodal coordinate reference node and the liquid kinetic equations are derived in the total Lagrangian formulation, which can easily be combined with the solid nonlinear finite element and the multi-body system algorithms. The free sliding and non-penetrating boundary constraint equations for rectangular tank are derived. To ensure the stability and the conservation of the solution in long time simulations, the system dynamic equations are solved by Bathe integral scheme. Three numerical examples are used to verify the effectiveness of the proposed method, including the free spreading of a square liquid column and the large amplitude sloshing of liquid under rotational and horizontal excitations. A good consistency is obtained by comparing the calculated results with experimental and other numerical results reported in the literature.