SPH–FV coupling algorithm for solving multi-scale three-dimensional free-surface flows

In two previous papers we presented an algorithm for coupling the Finite Volume (FV) method for the solution of 2D Navier–Stokes equations discretized on block structured Eulerian grids with the weakly-compressible Lagrangian Smoothed Particle Hydrodynamics (SPH) method. This coupling procedure exploits the SPH method to discretize flow regions close to free-surfaces and the Finite Volume approach to resolve both the bulk flow and the wall regions, where grid stretching can be favourably used. The information exchange between the two numerical schemes is established through overlapping zones. In the present paper this coupling paradigm is extended to a 3D framework. To this purpose, the extension of the algorithms for particle creation/deletion on the interfaces are described and issues related to free-surface intersection with each sub-domain boundary are addressed. Moreover, a new coupling procedure that simplifies the algorithm is proposed and tested. Effectiveness and accuracy achieved by the coupled solver are tested on challenging problems involving large free surface deformations and vorticity generation like the 3D flow past a cylinder below a free surface, the breaking wave generated by a ship bow in forward motion and the impact of a flat plate on the water surface.