Fluid sloshing in rectangular vessels with side-wall baffles using conformal mappings of multiply-connected domains

This paper focuses on the problem of inviscid, irrotational, incompressible fluid sloshing in a rectangular vessel with rigid, impermeable side-wall baffles, and investigates the feasibility of using time-dependent conformal mappings to numerically simulate the evolution of the unknown free-surface in fully-dynamic simulations. An algorithm which uses conformal mappings of a multiply-connected domain to relate the conjugate harmonic functions along the free-surface is documented, and kinematic results presented for a prescribed free-surface motion. The results show that the specific mapping for an infinite depth fluid has one free, within specific bounds, mapping parameter, while the mapping for finite depth fluids has two free mapping parameters. It is shown that having two free parameters gives a wider range of situations under which the conformal mapping can be computed, and it is concluded that the finite depth mapping should be used (in the appropriate limit) even for infinite depth simulations. Overall it is found that a computationally efficient algorithm can be devised to relate the conjugate harmonic functions along the free-surface of the flow domain.