Reconstruction of 3D Floating Body Motion on Shallow Water Flows Using the Smoothed Particle Hydrodynamics Method

Abstract

The investigation of floating body motions is a frequently visited topic in the areas of wave energy converters and coastal engineering. In fluvial conditions, the design process of floating platforms and the forecast of ice jamming events are also parts of relevant applications. Apparently, the two-way coupling of the fluid and floating body forces is often a fundamental requirement in such applications leading to computationally expensive studies. In cases of open surface flow modeling, where the water depth is sufficiently small compared to the horizontal extensions of a water body, the depth-averaged shallow water equations (SWE) offer an efficient alternative of the 3D Navier-Stokes equations. Utilizing the benefits of the SWEs, we aim to reduce the 3D problem of floating body motions to the 2D shallow water framework utilizing the smoothed particle hydrodynamic (SPH) method. However, the task is not straightforward due to the explicit nature of the SWE-SPH model. As an additional constraint, the presence of a floating object determines the local water depth, which is otherwise purely driven by the equation of motion and continuity. In our model, this constraint is defined by an additional penalty term in the equation of motion to accurately predict the water depth as well as the forces acting on the floating object. As a result, a two-way coupled fluid structure interaction model is established. The proposed method is easy to be implemented and offers an efficient alternative approach to the fully resolved computations, with a reasonable loss of accuracy.