Hybrid SW-NS SPH models using open boundary conditions for simulation of free-surface flows

Balancing the trade-off between the simulation detail and the computational efficiency in a hydrodynamic numerical model is generally difficult, e.g., one can hardly find a single set of governing equations that is capable of efficiently describing the wave propagation processes from offshore to nearshore and accurately presenting the details of wave breaking and interacting with coastal structures simultaneously. To address this predicament, open boundary coupling schemes are proposed in this paper to hybridize a SWE (shallow water equations)-based SPH (Smoothed Particle Hydrodynamics) model with a NS (Navier-Stokes) equations-based SPH model. The NS-SPH model is used to present the nonlinear hydrodynamic features in the main study domains, while the remaining domains are simulated with the SWE-SPH model, which calculates much faster than the NS-SPH model. The hybrid SPH models are applied to simulate solitary wave propagation, steady flows over a bump, dam breaking waves and standing waves. The hybridization performance on the information transmitting, mass and energy conservation, simulation detail, computational accuracy, computational efficiency and computational convergence speed is fully validated and evaluated. The results indicate that the proposed open boundary coupling schemes are capable of improving the computational efficiency on the premise of computational accuracy and simulation detail.