Three-dimensional kinematic open boundaries for multi-directional wave simulations in SPH

Mesh-free Lagrangian methods including smoothed particle hydrodynamics (SPH) are ideal for complex ocean engineering involving large free-surface deformations, yet their high computational cost in 3D large-scale domains remains a barrier. Hybrid coupling strategies combine mesh-based far-field solvers with near-field SPH to offer a solution; however, a core challenge has been maintaining consistent free-surface tracking along 3D interfaces under multi-directional waves. This study proposes a robust open boundary condition for multi-directional waves within a coupling framework between the fully nonlinear potential flow (FNPF) solver, OceanWave3D, and the SPH solver, DualSPHysics. Unlike conventional methods that often restrict boundary particle movement to the horizontal plane, the proposed algorithm prescribes all three velocity components derived from the FNPF model. This allows buffer particles to follow the fluid’s orbital motion, enabling stable tracking of the evolving free surface without requiring complex particle generation or removal routines. The method is demonstrated through three test cases: second-order Stokes waves, third-order doubly-periodic waves, and a vertical jet breaking. Results show that the approach effectively suppresses unphysical numerical artefacts, such as unphysical vortices, while accurately capturing complex phenomena like Stokes drift and high-velocity jetting during curvature collapse. Within its intended scope of local, finite-duration SPH simulations, this one-way coupling framework provides a simple and stable approach for high-fidelity 3D simulations, ensuring essential wave kinematics and nonlinear dynamics are captured with high physical integrity across a range of sea states.