A 3D parallel Particle-In-Cell solver for wave interaction with vertical cylinders

In this paper, the Particle-In-Cell (PIC) based PICIN solver is extended to three spatial dimensions and parallelised using the Message Passing Interface (MPI) approach. The PICIN solver employs both Eulerian grid and Lagrangian particles to solve the incompressible Navier-Stokes equations for free-surface flows. The particles are employed to carry all the fluid properties, solve the non-linear advection term and track the free-surface, while the grid is used solely for computational efficiency in solving the non-advection terms. Validation of the new 3D model concentrates on test cases involving multiple wave types (including regular waves, focused waves and solitary waves) interacting with vertical cylinders in several spatial configurations. The results are compared with laboratory data and numerical results from state-of-the-art Volume of Fluid (VOF) based Eulerian solvers such as those from the OpenFOAM® suite. It is shown that the 3D parallel PICIN model is able to well simulate highly non-linear water waves, and the interaction of such waves with vertical cylinders, with a CPU efficiency similar to Eulerian solvers. Moreover, the innovative use of particles in PICIN, akin to meshless Lagrangian solvers, gives the model a particular flexibility in handling complex, full 3D, water-wave scenarios involving large free-surface deformations.