New smoothed particle hydrodynamics (SPH) formulation for modeling heat conduction with solidification and melting

When modeling the phase change, the latent heat released (absorbed) during solidification (melting) must be included in the heat transfer equation. In this paper, different smoothed particle hydrodynamics (SPH) methods for the implementation of latent heat, in the context of transient heat conduction, are derived and tested. First, SPH discretizations of two finite element methods are presented, but these prove to be computationally expensive. Then, by starting from a simple approximation and enhancing accuracy using different numerical treatments, a new SPH method is introduced, that is fast and easy to implement. An evaluation of this new method on various analytical and numerical results confirms its accuracy and robustness.