Numerical sloshing simulations: Comparison between lagrangian and lumped mass models applied to two compartments with mass transfer

In the present paper, 2D numerical simulation of sloshing waves coupled to the flooding flow between two compartments is carried out employing lumped mass and Lagrangian methods. The first method used is a Lumped Mass method with a moving free surface (LM), which is based on the motion equations for the gravity centre of mass within a compartment. In this method, the free surface is modelled as a planar surface, with limited degrees of freedom. The second one is the so-called Moving Particle Semi-Implicit (MPS) method, a robust method based on particle interactions in a Lagrangian coordinate system. Sloshing simulations are performed within a closed domain, in which the free surface is modelled as a deformable surface for a single-phase flow. An improved boundary wall condition scheme is applied. By applying these two methods the hydrodynamic features of the sloshing flow under sway and roll motion and several water levels are investigated. The excitation frequencies are set near the natural wave frequencies. Furthermore, the complexity added to the sloshing wave by the flow exchange passing through an opening are reported, taking into account two opening configurations. The numerical results are validated by corresponding experimental data. Comparison of the numerical results against the experimental data shows, in general, good agreement. Two main stages of accuracy levels are observed for lower and higher frequencies. At the first stage, the Lumped Mass and the Moving Particle Semi-Implicit methods present similar results, whereas at the last stage the MPS model is seen to be more suitable for the sloshing simulations, in which wave breaking is the dominant phenomenon.