ISPH Numerical Modeling of Nonlinear Wave Run-up on Steep Slopes

Non-breaking tsunami waves run-up on steep slopes can cause severe damages to coastal structures. The estimation of the wave run-up rate caused by tsunami waves are important to understand the performance and safety issues of the breakwater in practice. In this paper, an Incompressible Smoothed Particle Hydrodynamics method (ISPH) method was utilized for the 2DV numerical modeling of nonlinear wave run-up on steep slopes. SPH is a meshless method based on particles, which is capable of high accurate modeling of free surface flows with large deformations. In developed model, mass and momentum conservation equations were solved in a Lagrangian form using a two-step fractional method. In the first step, Navier-Stokes equations were solved to compute velocity components by omitting pressure term and in the absence of incompressible condition. In the second step, the continuity constraint was satisfied and the resulting Poisson equation was solved to calculate pressure terms. Velocity values were then corrected and surface positions were computed. In the present model, a new technique was applied to allocate density to the particles for the calculations. By employing this technique, ISPH model was stablized. The developed ISPH model was first validated by the solitary wave propagation on the constant water depth and the corresponding results showed good agreement with analytical results. The convergence of the method and the sensitivity of relevant model parameters were discussed. Then, validated model was used to study the run-up of solitary waves on steep slopes by considering a coastal breakwater for various wall steepnesses (i.e. 1:1, 2:1, 4:1, 8:1 and vertical wall).