Mesh-free simulation of liquid sloshing subjected to harmonic excitations

In this study a mesh-free numerical model for simulating 3-D free-surface potential flows is established. A time-marching scheme in Lagrangian aspect is chosen for the specification of boundary conditions on the moving and deforming free surface while a local polynomial collocation method is applied for solving the Laplace equation at each time step. This collocation method is employed because the partial derivatives of the solution are calculated accurately. The trajectory of each free-surface node can thus be predicted precisely due to the accurate estimation of the partial derivatives of velocity potential, which represent components of the velocity vector at that specific node. The numerical model is applied to the simulation of free surface waves by the liquid sloshing in rectangular, square and cylindrical swaying tanks. Fairly good agreements are observed in the comparison of numerical results with experimental data. Because the partial derivatives of the velocity components are accurately calculated, the pressure distribution in the domain can also be acquired by solving the pressure Poisson equation separately.