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

摘要

When modelling phase change, the latent heat released (absorbed) duringsolidification (melting) must be included in the heat transfer equation. Inthis paper, different SPH methods for the implementation of latent heat, in thecontext of transient heat conduction, are derived and tested. First, SPHdiscretizations of two finite element methods are presented, but these prove tobe computationally expensive. Then, by starting from a simple approximation andenhancing accuracy using different numerical treatments, a new SPH method isintroduced, that is fast and easy to implement. An evaluation of this newmethod on various analytical and numerical results confirms its accuracy androbustness.