ISPH wave simulation by using an internal wave maker

• A non-reflection internal wave maker is introduced into the ISPH method.
• Technical details for the implementation of present wave maker are presented.
• The model is verified by the applications to propagating and standing waves.
• Long time wave-structure interaction and wave decomposition is simulated.

In this paper, a non-reflection internal wave maker algorithm is included in the incompressible Smoothed Particle Hydrodynamics (ISPH) model for the wave simulations. A momentum source term derived from the Boussinesq equations is employed and added into the Lagrangian form of Navier–Stokes equations for the wave generations that are not affected by the reflected waves. In this work, the technical details of implementing the internal force into the ISPH equations are proposed and a series of numerical tests are carried out for the selection of relevant parameters and investigation of their sensitivities in different wave conditions. In model applications, the problems of wave propagation and reflection from a vertical wall are studied to verify the model performance in standing wave generations and the non-reflection characteristics of the internal wave maker. Furthermore, a more challenging wave decomposition process over a trapezoid breakwater is presented, which has not been fully investigated by other similar particle-based methods. The simulation results of wave surface profile on six wave gauges agree well with the experimental results and this shows that the present model with the non-reflection internal wave maker can provide a more robust particle modeling tool for the long time simulation of wave and wave–structure interactions.