SPH no-slip BC implementation analysis at the continuous level

The aim of this paper is to discuss whether there are structural problems in three of the most representative velocity mirroring techniques used to force no-slip boundary conditions (BC) in SPH for Newtonian incompressible flows. We refer specifically to fixed fluid particles, ghost particles, and Takeda et al. [1] boundary integrals. In Newtonian incompressible flows, the viscous related terms in the momentum conservation equation depend on the evaluation of the Laplacian of the velocity field. In order to analyze such techniques, the continuous version of the Laplacian approximation by Morris et al. [2] and Monaghan-Cleary-Gingold [3] viscous terms has been considered. It has been shown that there are intrinsic inaccuracies in the computation of the Laplacian close to the boundaries and the onset of singularities in such evaluation for some flows and mirroring techniques combinations. The impact of these deviations in the SPH simulation of viscous flows is not clear at this stage.