Two novel ways to impose free-slip boundary conditions in fluid-structure interaction problems using the Particle Finite Element Method

As well known, the imposition of boundary conditions is, in many cases, the trickiest part in solving differential problems, both from a physical and numerical standpoint.
This work focuses on the way boundary conditions are accounted for in the solution of fluid-structure interaction problems using the Particle Finite Element Method (PFEM). In particular, the PFEM traditionally employs no-slip conditions on the fluid-solid interfaces.
Our aim is twofold. On the one hand, we demonstrate that, in the framework of the PFEM, the no-slip hypothesis is too strong in some cases, leading to erroneous physical results, and that a free-slip condition is to be preferred instead; we therefore propose two novel ways to impose free-slip conditions, devoting special attention to generality, simplicity and robustness. On the other hand, we show how the use of free-slip boundary conditions can also be beneficial with regards to two major problems arising from the remeshing procedure employed by the PFEM: the violation of the mass conservation principle and the introduction of spurious pressure oscillations.