Modelling free surface flows with smoothed particle hydrodynamics

In this paper the method of Smoothed Particle Hydrodynamics (SPH) is extended to include an adaptive density kernel estimation (ADKE) procedure. It is shown that for a van der Waals (vdW) fluid, this method can be used to deal with free-surface phenomena without difficulties. In particular, arbitrary moving boundaries can be easily handled because surface tension is effectively simulated by the cohesive pressure forces. Moreover, the ADKE method is seen to increase both the accuracy and stability of SPH since it allows the width of the kernel interpolant to vary locally in a way that only the minimum necessary smoothing is applied at and near free surfaces and sharp fluid-fluid interfaces. The method is robust and easy to implement. Examples of its resolving power are given for both the formation of a circular liquid drop under surface tension and the nonlinear oscillation of excited drops. Key words: gas-liquid and vacuum-liquid interfaces, surface tension and related phenomena, heat conduction, computational methods in fluid dynamics