An ISPH with modified k–ε closure for simulating breaking periodic waves

Abstract

The Incompressible Smoothed Particle Hydrodynamics (ISPH) method, solving the 2D RANS (Reynolds Averaged Navier-Stokes) equations with the modified k–ε turbulence closure developed by Wang and Liu (2020) [ Coastal Engineering , 157, 1–28], is further extended to periodic waves. The capability of this numerical model is demonstrated by applying it to three laboratory experiments: (1) Dynamics of surf-zone turbulence generated by a spilling breaker and a plunging breaker over a plane slope in small-scale wave flume experiments, (2) breaking wave generated turbulence over a stationary barred beach in large-scale wave flume experiments, and (3) spatial and temporal distributions of turbulence generated by bi-chromatic breaking waves over a submerged stationary barred slope in medium-scale wave flume experiments. In this new ISPH model, the gradient correction_ dynamically stabilized scheme is adopted to reduce numerical dissipation. The experimental data for the spilling breaker on a plane beach is used to calibrate the model. Once the model is calibrated, all the empirical coefficients in the turbulence closure model, including the stress limiter coefficient λ 3 , which is required in modifying the eddy viscosity, are fixed for the validation processes with other experimental data sets. All model-data comparisons are made in terms of free surface profile, mean velocity field and turbulent kinetic energy. The differences between experimental observations and numerical simulations are quantified by the percentage error. Overall, good agreement is observed for all experiments. This paper presents the first comprehensively validated 2D ISPH model with the modified k–ε turbulence closure, which can be applied to periodic wave breaking problems. • The Incompressible Smoothed Particle Hydrodynamics (ISPH) method is coupled with the modified k–ε turbulence closure equations to solve the 2D RANS (Reynolds Averaged Navier-Stokes) equations. The gradient correction_ dynamically stabilized scheme is adopted to reduce numerical dissipation. • The model has been checked with three laboratory experiments for periodic breaking waves. (1) Spilling and plunging cnoidal waves over a plane slope in small-scale wave flume experiments, (2) plunging periodic breaking wave over a stationary barred beach in large-scale wave flume experiments, and (3) bi-chromatic breaking waves over a submerged stationary barred slope in medium-scale wave flume experiments. • All model-data comparisons are made in terms of free surface profile, mean velocity field and turbulent kinetic energy. • The differences between experimental observations and numerical simulations are quantified by the percentage error. • Overall, good agreement is observed for all experiments. Good agreements are observed in terms of free surface profile, mean velocity field, vorticity field, turbulent kinetic energy and turbulent shear stress.