Attitude motion and nonlinear free-surface deformation of stone-skipping over shallow water

Stone-skipping is a common yet complex motion that involves rigid-body dynamics and fluid–structure interaction (FSI). While many computational fluid dynamics methods are used to simulate the interaction between a stone and fluid, little research has been done to consider the stone, fluid, and fluid boundary as a whole in a simulation. This study, focuses on the attitude motion and free-surface deformation of stone-skipping over shallow water to investigate how the boundary effect of FSI impacts ricochet behaviors. Initially, we establish an iteration framework for the stone-skipping FSI issue based on a weakly compressible smoothed particle hydrodynamics (SPH) method with a Riemann solver. We conduct particle-independence verification and simulate several cases under varying water heights. Additionally, we analyze and compare ricochets in deep and shallow cases with different incident angles and initial pitch angles. The numerical results demonstrate that in shallow flow scenarios, the “comma-shaped” high-pressure area is compressed by the stone and the fluid boundary, leading to a more moderate variation in pitch angle. Stone-skipping in shallow water typically covers a shorter distance and reaches a lower height compared to deep water cases. Changes in the incident angle show that shallow water hinders successful skipping. Futhermore, different initial pitch angles reveal that water height directly impact the stone's trajectory in both horizontal and vertical directions. These highlight the connection between motion patterns and parameters, offering a reliable numerical prediction for the stone-skipping problem using the Riemann SPH method.