Simulation of near-shore solitary wave mechanics by an incompressible SPH method

An incompressible smoothed particle hydrodynamics (SPH) method together with a large eddy simulation (LES) approach is used to simulate the near-shore solitary wave mechanics. The incompressible Navier–Stokes equations in Lagrangian form are solved using a two-step fractional method. This method first integrates the velocity field in time without enforcing incompressibility. The resulting deviation in particle density is projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation. SPH formulations are employed for discretization of relevant gradient and divergence operators. The spatial filtering of the LES approach produces sub-particle scale stresses, which are treated by the Smagorinsky model. The cases of a solitary wave against a vertical wall and running up a plane slope are treated. The wave profiles are in good agreement with reported experimental data or analytical solutions. It is found that the assumption of hydrostatic pressure holds almost everywhere except during the last stages of wave breaking. The dynamic viscosity is also found to be a maximum near the breaking front.