Viscous flow past a circular cylinder close to a free surface: results from a benchmark between SPH and mesh-based solvers

Flow past a circular cylinder close to a free surface at a Reynolds number of 180 is numerically investigated in this paper. While the fully submerged conditions for such flow are well established, adding a free surface, and setting the submergence ratio and the Froude number in specific ranges, it induces a challenging free-surface dynamics with wave breaking phenomena. In literature reference solutions obtained with a Volume of Fluid (VOF) approach are available. Those reference data, for specific conditions, show classical vortex shedding which are related to oscillations of the lift force, accompanied with intriguing low frequency subharmonic modes called metastable. The latter are related to the onset of alternating states in the cylinder wake. In the present work, the metastable mode is investigated with two SPH variants and two mesh-based solvers. These solvers are themselves representatives of various numerical models, namely Finite Volume Method with VOF and level set free-surface capturing/tracking techniques, and ?-SPH, with and without shifting and multi-resolution capabilities. The solutions provided are affected by large discrepancies. Those one are documented and some explanations hinted. The case is here proposed as a benchmark for SPH solvers characterized by the presence of inlet/outlet boundary conditions and an unsteady free surface.