The nonlinear viscous flow generated from forced heaving oscillation of 2D floating body in calm water is carried out numerically using Improved Meshless Local Petrov-Galerkin (IMLPG_R) method based on Rankine Source function. In the present particle-based method, the gradient calculation has been improved using ghost particle method. However, for estimating pressure, only single layer of the boundary particles are used. This is the first paper to extend the application of the IMLPG_R for heave oscillations of the floating body. Simulations are carried out for vertical oscillation of rectangular shaped mono hull and twin hull. Hydrodynamics of these hulls for various amplitude and frequency of oscillations are performed and the numerical results agree well with existing literature results.
The fluid dynamics associated with oscillation of floating structures on the free surface of a viscous fluid is a topic of great interest, because of the complexity involved in solving equations of motion of floating body and fluid particle movement simultaneously. Yeung and Ananthakrishnan (1992 and 1997), Yeung et al., (1998) and Ananthakrishnan (1999,2012 and 2015) had numerically simulated various free surface flow problems associated with oscillation of floating bodies in the free surface of calm water. Analysis related to oscillation of floating structure is significant for the design and development of floating bodies such as ships, offshore platforms, barges, floating- breakwater, fish-farms, and floating airports in coastal and ocean engineering.
In fluid structure interaction problems, two numerical models are commonly using for fluid phase, one is based on fully nonlinear potential flow theory (FNPT) and another is based on Navier-Stokes (NS) equations. Many numerical methods are developed for solving these equations. These methods are grouped into mesh-based methods and mesh-free methods. Various mesh-based methods such as finite element, finite difference and finite volume methods are used to solve these numerical models. Even though all of these methods produced impressive results, a limitation of mesh-based methods is that a computational grid is required and needs to be managed. Their success largely depends on good quality meshes. Depending on the formulation, the mesh may need to be updated repeatedly or to be refined to follow the motion of the free surface and need to be maintained to get a good result. This is a time-consuming task and expensive, particularly in the cases with breaking waves. The mesh-free method is an alternative method, which can overcome the problems associated with the mesh- based method. Instead of discretizing the computational domain into grids, mesh-free method discretizing the fluid domain into randomly distributed nodes to construct appropriate solutions. So the limitations associated with mesh does not exist.