Viscous Flow Past a NACA0012 Foil Below a Free Surface Through the Delta-Plus-SPH Method

The present work is dedicated to the modeling of viscous flow past a NACA0012 foil fixed in a current below a free surface. To this end, the [Formula: see text]-smoothed-particle hydrodynamics (SPH) model has been adopted. This SPH model prevents the inception of the numerical tensile instability in the flow region characterized by negative pressure since a tensile instability control (TIC) has been included. In the TIC, a pressure differencing formulation (PDF) has been adopted for the momentum equation in the flow region characterized by negative pressure. In order to completely remove the numerical noise in the vorticity field, in this work, the PDF is also applied for the region with positive pressure, but except for the free-surface region in order to ensure the free surface stability when wave breaking occurs. The mechanism of PDF being able to eliminate the numerical noise in the vorticity field is also briefly analyzed. In order to reduce the nonconservation of total momentum induced by the PDF, a particle-shifting technique (PST) is implemented in each time step for regularizing the particle position. In the numerical results, [Formula: see text]-SPH results are validated by the experimental data and other verified numerical results. Improvements of the results of [Formula: see text]-SPH with PDF with respect to the ones without using PDF are demonstrated. Parametrical studies based on the [Formula: see text]-SPH model regarding the breaking and non-breaking waves generated by the flow past a submerged foil are also carried out.