Abstract
In this paper 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 boundary conditions of 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 governing equation is satisfied on boundaries as well as boundary conditions are so the partial derivatives of the solution are calculated accurately. The trajectories of free-surface nodes 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 in the liquid sloshing of both rectangular and cylindrical swaying tanks. Fairly good agreements are observed in the comparison of numerical results with experimental data.
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