A coupled FV-SPH approach to simulate the flow around a vertical free-surface piercing cylinder

This paper presents an improved coupled Finite-Volume/Smoothed Particle Hydrodynamics (FV–SPH) methodology for simulating complex free-surface flows around rigid bodies, targeting cases where strong free-surface deformation coexists with the need to accurately resolve boundary-layer vorticity generation and wake dynamics. The domain is decomposed so that SPH is employed only in regions dominated by relevant free-surface evolution, while an Eulerian FV solver on a multi-block structured grid is used elsewhere; information is exchanged through interpolation-based boundary transfer and a blending region that progressively matches SPH and FV fields. Two key extensions are introduced: (i) a refined open-boundary particle injection strategy that aligns injected particles with the level-set free-surface position derived from FV data, improving the free-surface representation across open boundaries; and (ii) forcing of SPH particles within an annulus around the cylinder to preserve FV accuracy in the near-wall boundary layer. The method is validated against experiments for flow past a free-surface piercing vertical cylinder at Fr = 0.713 and Re = 17,840, capturing the upstream free-surface rise, downstream depression, hydraulic-jump boundaries, and coherent vortical structures (including a horseshoe vortex) with good agreement in free-surface elevation along the flume midline