Abstract: Application of the Smoothed Particle Hydrodynamics (SPH) in solving the Shallow Water Equations (SWE) holds a great potential, particularly in the field of ocean numerical simulations, but the issues of the SWE-SPH method related to open boundaries remain unresolved. This study addresses the problem of reflection at an open boundary in previous SWE-SPH models, and describes a new method for treating non-reflective boundaries based on the Flather condition of gravity wave open boundaries. We evaluate the performance of this new boundary condition using three classical numerical simulation cases－steady flow over a bump, wave propagation of sea level perturbations in a flat-bottom channel with two open ends, and flow around a circular cylinder－and compare it with the conditions in the original method. Results indicate that for an open boundary, the new condition reduces its reflections effectively, allows propagating disturbances to cross it outward, and facilitates implementation of its external flow conditions specified. We have applied the improved SWE-SPH model to simulations of the Okushiri tsunami, and compared the results with those of the finite volume method. This proves it is applicable and effective in handling complicated depth and trans-critical flow simulations, thus expanding the scope of ocean numerical simulations.

Key words: Smoothed Particle Hydrodynamics (SPH), Shallow Water Equations (SWE), open boundary condition, numerical simulation