Abstract
This paper presents a numerical model for simulating wave run-up on rough sloping surfaces. Incompressible smoothed particle hydrodynamics (ISPH) has been utilized, which is capable of efficient tracking of free surface deformation in a Lagrangian coordinate system. Many of the existing models have focused on inviscid wave run-up on a smooth surface, but few numerical models and especially experimental studies have investigated the effect of beach roughness on the run up. In the present study two methods have been deployed to study the effect of roughness on wave run up. In the first method, the mass unit force, which is a coefficient of the fluid viscosity, and is dependent on the roughness of the solid boundary, has been used. In the second method, mass unit force obtained from the wall functions was utilized to enforce the friction on the particles near the boundaries. The comparisons of the numerical simulations with the analytical solutions and experimental data confirmed the capability of the model in simulating wave propagation and wave breaking. It was also concluded that the effect of roughness on wave run up depends on both the roughness itself and the beach slope. The results also indicated small roughness effect on waves running up over steep slopes.
Highlights
The problem of determining the run-up of solitary waves over beaches usually arises in the study of the coastal effects of tsunamis
The nonlinear shallow water equations (NSWE) describe a thin layer of fluid of constant density in hydrostatic balance, bounded from below by bottom topography and from above by a free surface
The model is capable of simulating the propagation of solitary and regular waves. It is capable of simulating the whole process of wave propagation, shoaling, breaking and run-up on beach slopes
Summary
The problem of determining the run-up of solitary waves over beaches usually arises in the study of the coastal effects of tsunamis. In the early simulations of fluid flows by the weakly compressible SPH, incompressibility was realized through an equation of state so that the fluid was assumed slightly compressible. In this case, a large sound speed has to be introduced, which could cause problems of sound wave reflections at the solid boundaries. Many of the existing models have focused on inviscid wave run-up on smooth surfaces, but there have been a few numerical and experimental studies which are carried out to investigate how beach roughness affects the run up. This paper presents an incompressible two-dimensional SPH model to simulate the wave run-up on smooth and rough slopes. Their laboratory studies yielded formulations to assess various run up levels as a function of the surf similarity or breaker parameter
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