Coupling weakly-compressible SPH with Finite Volume Method: an algorithm for simulating free-surface flows

An algorithm for coupling a classical Finite Volume (FV) approach, that discretize the Navier-Stokes equations on a block structured Eulerian grid, with the weakly-compressible SPH is presented. The coupling procedure aims at applying each solver in the region where its intrinsic characteristics can be exploited in the most efficient and accurate way: the FV solver is used to resolve the bulk flow and the wall regions, whereas the SPH solver is implemented in the free surface region to capture details of the front evolution. In order to avoid the difficulties connected with inhomogeneous domain decomposition, in both SPH and FV regions a weakly compressible flow model was firstly tested. However, the coupling procedure has been implemented in order to allow the adoption of different time steps between the two solvers. Thanks to this feature, it will be shown that the proposed technique is also able to reproduce an inhomogeneous coupling. Indeed, the FV solver, because of the space discretization adopted and the implicit time integration, naturally tends to an incompressible discrete solver, wherever the time step is much larger of what required to capture compressibility effects. The different coupling strategies as well as convergence studies have been carried out in the 2D framework. The reported results clearly prove that the combined use of the two solvers is convenient from the point of view of both accuracy and computing time.