Variational domain decomposition scheme for linear Stokes-Joukowski potentials of fluid in baffled tanks

Sloshing-induced force and moment may affect the dynamic property of the liquid-contained system. Analytically presented linear Stokes-Joukowski potentials of fluid are usually needed for analytical study of sloshing in liquid-filled tank under rotational (e.g., pitching) excitations. To obtain the analytically approximate linear Stokes-Joukowski potentials of fluid in the rigid baffled tanks, a variational domain-decomposition scheme is proposed. This scheme includes three steps: (i) dividing the hydrostatic baffled fluid domain into simple sub-domains based on the positions of the baffles (i.e., using the baffle as part of the boundaries of the sub-domain) by introducing artificial interfaces and densities of fluids in the different sub-domains or auxiliary normal fluid velocity functions on the artificial interfaces; (ii) expressing the solution for linear Stokes-Joukowski potential of each sub-domain as a linear combination of a class of harmonic functions with undetermined coefficients, and expressing the auxiliary normal fluid velocity functions on the artificial interfaces as Fourier-type series with undetermined coefficients; (iii) solving the undetermined coefficients by the Trefftz method and the proposed variational formulations. The obtained semi-analytical linear Stokes-Joukowski potential agrees well with that published in literature or given by finite element method (FEM), and its applicability to study nonlinear sloshing problem is verified by applying it to a two-dimensional partially fluid-filled rectangular tank with a T-shaped baffle under pitching excitation. The present semi-analytical result is compared with that given by computational fluid dynamics (CFD) software or literature.