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Modeling phase change problems numerically is vital for understanding manynatural (e.g., ice formation, steam generation) and engineering processes(e.g., casting, welding, additive manufacturing). Almost all phase changematerials (PCMs) exhibit density/volume changes during melting, solidification,boiling, or condensation, causing additional fluid flow during this transition.Most numerical works consider only two phase flows (either solid-liquid orliquid-gas) for modeling phase change phenomena and some also neglectvolume/density change of PCMs in the models. This paper presents a novel lowMach enthalpy method for simulating solidification and melting problems withvariable thermophysical properties, including density. Additionally, thisformulation allows coupling a solid-liquid PCM with a gas phase in order tosimulate the free surface dynamics of PCMs undergoing melting andsolidification. We revisit the two-phase Stefan problem involving a densityjump between two material phases. We propose a possible means to include thekinetic energy jump in the Stefan condition while still allowing for ananalytical solution. The new low Mach enthalpy method is validated againstanalytical solutions for a PCM undergoing a large density change during itsphase transition. Additionally, a few simple sanity checks are proposed tobenchmark computational fluid dynamics (CFD) algorithms that aim to capture thevolume change effects of PCMs.

A low Mach enthalpy method to model non-isothermal gas-liquid-solid flows with melting and solidification