Simulation of Gravity Wave Propagation in Free Surface Flows by an Incompressible SPH Algorithm

This paper presents an incompressible smoothed particle hydrodynamics (SPH) model to simulate wave propagation in a free surface flow. The Navier-Stokes equations are solved in a Lagrangian framework using a three-step fractional method. In the first step, a temporary velocity field is provided according to the relevant body forces. This velocity field is renewed in the second step to include the viscosity effects. A  Poisson equation is employed in the third step as an alternative for the equation of state in order to evaluate pressure. This Poisson equation considers a trade-off between density and pressure which is utilized in the third step to impose the incompressibility effect. The computations are compared with the experimental as well as numerical data and a good agreement is observed. In order to validate proposed algorithm, a dam-break problem is solved as a benchmark solution and the computational results are compared with the previous numerical ones.