A variational domain decomposition scheme for the natural sloshing modes in the baffled tanks

Abstract

A variational domain-decomposition scheme is presented to obtain the analytically approximate natural sloshing modes in the rigid baffled tanks. The scheme consists of three steps: (i) dividing the unperturbed complicated liquid domain into several simple sub-domains by introducing artificial interfaces, and auxiliary artificial non-dimensional densities of fluids in these sub-domains are also introduced; (ii) obtaining spectral matrix problem by combing the approximate variational formulation of the approximate natural sloshing problem with the Trefftz method, eigenvalues of the spectral matrix problem are computed and plotted; (iii) extracting the pursued analytically approximate natural sloshing modes from the eigenfunctions given by the spectral matrix problem with artificial non-dimensional densities sufficiently close to 1. The fluid velocity potential in each sub-domain is expressed as a linear combination of a set of harmonic functions with unknown weight coefficients. A variational principle for natural sloshing of multi-layer immiscible fluid with multi free surface is developed and modified to be employed in step (ii). The extraction of the pursued analytically approximate natural sloshing modes is realized by classifying the obtained spectral parameters into two classes, one of which is dominated by the free-surface wave effect, whereas the other one is dominated by the effect of the artificial interfaces between adjacent sub-domains. To verify the present scheme, the results obtained are compared with results published or given by finite element analysis.