Computer modeling of liquid-solid impacts

A mathematical model is formulated in the framework of the potential theory to describe the impact of a bore on a rigid wall. The solution of the resulting free-interface flow problem is numerically approximated by a tracking method of new conception. Basically, the free interface separating liquid and air is assumed to be a free fluid line. Its shape and location are tracked in time by numerically solving the evolutive equations of a set of interface node positions and potentials. The evolutive equations are derived from Bernoulli’s law and are integrated by the Crank–Nicholson method. As the shape of the computational domain evolves in time, the domain is fully re-meshed at each time step, and a new steady mixed Dirichlet–Neumann Laplacian problem is formulated and solved by applying the RT0 mixed finite element method. This potential flow solver has been validated by simulating the liquid–solid impact of a bore against a rigid wall and comparing the numerical results with the available experimental measurements.