Numerical studies of complex fluid-solid interactions with a six degrees of freedom quaternion-based solver in the SPH framework

Abstract

Six-degree-of-freedom (6-DOF) motions of structures widely exist in aeronautics and ocean engineering. It is significant to study the 6-DOF motion for simulating the trajectory and impact load of structures. This paper uses the smoothed particle hydrodynamics (SPH) method combined with some modified numerical techniques to simulate the fluid-solid interactions (FSI), then a quaternion-based method is adopted to simulate the free motion of rigid bodies, where the calculation process of 6-DOF motions based on quaternion is elaborated in detail. The accuracy of this method is verified through two benchmark tests, including water entry of a cuboid and skipping stone, which can prove the pressure calculation and motion prediction of rigid bodies are consistent with the experimental results. At last, the 6-DOF ditching process of a seaplane is simulated by the quaternion method embedded in the SPH model, and the simulation results are consistent with those simulated by the finite volume method (FVM). The above three tests demonstrate that the SPH model combined with a 6-DOF quaternion-based solver can accurately solve FSI problems from basic to complex at different scales. Besides, the SPH model shows significant advantages in capturing large-deformed free surfaces and splashing droplets compared with Eulerian-grid-based methods.