Enhancing smoothed particle hydrodynamics for shallow water equations on small scales by using the finite particle method

Abstract

The smoothed particle hydrodynamic (SPH) method is applied to the simulation of a small scale thin fluid film. The major influence of surface tension effects in small scales leads to the need of a method capable of accurately modeling third order derivatives. Previous results show that there are circumstances where SPH is not consistent, resulting in difficulties to calculate higher order derivatives. In order to resolve this, the SPH method is extended using the finite particle method which allows to consistently calculate derivatives up to a chosen order. The model is validated by comparing the stationary simulation of a small drop to the analytical solution.