### Abstract

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.

Original language | English |
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Pages (from-to) | 61-71 |

Number of pages | 11 |

Journal | European Journal of Mechanics, B/Fluids |

Volume | 61 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

### Keywords

- Body-water-impact
- Skipping stones
- SPH

### Cite this

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*European Journal of Mechanics, B/Fluids*, vol. 61, pp. 61-71. https://doi.org/10.1016/j.euromechflu.2016.10.001

**SPH simulation of skipping stones.** / Yan, Rui; Monaghan, J. J.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - SPH simulation of skipping stones

AU - Yan, Rui

AU - Monaghan, J. J.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Body-water-impact

KW - Skipping stones

KW - SPH

UR - http://www.scopus.com/inward/record.url?scp=84994759934&partnerID=8YFLogxK

U2 - 10.1016/j.euromechflu.2016.10.001

DO - 10.1016/j.euromechflu.2016.10.001

M3 - Article

VL - 61

SP - 61

EP - 71

JO - European Journal of Mechanics, B/Fluids

JF - European Journal of Mechanics, B/Fluids

SN - 0997-7546

ER -