Application of the unified semi-analytical wall boundary conditions to 2-D incompressible SPH

This work aims at improving an incompressible SPH model (ISPH) by adapting to it the unified semi-analytical wall boundary conditions proposed by Ferrand et al. [1]. The ISPH algorithm considered is the one proposed by Lind et al. [2]. The new description of the wall boundaries allows to impose accurately a von Neumann boundary condition on the pressure that corresponds to the impermeability condition. The shifting and free-surface detection algorithms are adapted to the new boundary conditions. A new way to compute the wall renormalisation factor in the frame of the unified semianalytical boundary conditions is proposed in order to decrease the computational time. We propose several 2-D verifications to the present approach. Our results were compared to analytical or other numerical results. We investigated the convergence of the method and proved its ability to model complex free-surface and turbulent flows. The results were generally improved compared to a weakly compressible SPH model with the same boundary conditions, especially in terms of pressure prediction, with a lower computational time.