Numerical Simulation of Surface Waves using Meshfree Methods

Abstract

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian-based numerical method used for simulating problems in fluid and solid mechanics. In this thesis, a basic introduction to particle and Smoothed Particle (SP) approximations is given first. Application of SP approximations to Euler and Navier-Stokes equations is discussed, followed by an improvement to restore first order consistency in SPH. Then, simulations of 2D free-surface waves in a weakly incompressible fluid are conducted. If the artificial viscosity used is small, results indicate that the accuracy of SPH scheme is reasonably good; however, a low artificial viscosity leads to a rugged air-water interface. Furthermore, application of the LES filter has negligible effects. It is also observed that the use of Renormalized SPH (R-SPH) increases diffusivity but does not increase accuracy significantly. Hence, for 2D surface waves in weakly incompressible fluids, basic SPH formulation without any modification is as good as the R-SPH or LES-SPH methods.