Simulation of 2D Free-surface Potential Flows Using a Robust Local Polynomial Collocation Method

In this paper a mesh-free numerical model for simulating 2D free-surface potential flows is established. A Lagrangian time-marching scheme 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. The collocation method is developed in a way that the governing equation is satisfied on boundaries as well as boundary conditions. At any free surface node, this gives accurate estimation of the derivatives of velocity potential, which represent components of the velocity vector at that specific node. Therefore, trajectories of the free surface nodes can be predicted precisely. The numerical model is applied to the simulation of free surface waves in the liquid sloshing of a swaying tank. Present model is verified by comparing the numerical results with experimental data. Fairly good agreements are observed.