SPH simulation of skipping stones

In this paper we simulate the motion of rigid bodies bouncing from the surface of water in two dimensions. A common example is the skipping of stones. Although this takes place in three dimensions the stone is normally spinning rapidly and the rapid spin stabilizes the stone so that the angle of a plane normal to the spin direction and fixed in the stone maintains a constant angle to the initial water surface. Because of this it is reasonable to expect that the motion in three dimensions is similar to that in two dimensions. Our SPH calculations confirm that this is the case. We simulate the successive skips by computing the free flight after a skip using simple particle dynamics, from which the initial conditions for the next impact can be predicted. This impact can then be treated as an impact in a new tank. As a result the number of SPH particles required to follow successive skips is massively decreased. The results are in satisfactory agreement with a simple theory which is the two dimensional analogue of a three dimensional theory. We also simulate the skipping of a curved plate, convex in the direction of flight, which mimics the base of a stone or sea shell. We find that the skipping is similar to that of a flat plate.