  This work expands on our recently introduced low Mach enthalpy method [1] for
simulating the melting and solidification of a phase change material (PCM)
alongside (or without) an ambient gas phase. The method captures PCM's volume
change (shrinkage or expansion) by accounting for density change-induced flows.
We present several improvements to the original work. First, we introduce
consistent time integration schemes for the mass, momentum, and enthalpy
equations, which enhance the method stability. Demonstrating the effectiveness
of this scheme, we show that a system free of external forces and heat sources
can conserve its initial mass, momentum, enthalpy, and phase composition. This
allows the system to transition from a non-isothermal, non-equilibrium,
phase-changing state to an isothermal, equilibrium state without exhibiting
unrealistic behavior. Furthermore, we show that the low Mach enthalpy method
accurately simulates thermocapillary flows without introducing spurious phase
changes. We propose an analytical model to validate advanced CFD codes for
simulating metal manufacturing processes like welding and 3D printing. These
processes involve a heat source melting metal or alloy in an inert gas
environment. Traditionally, validation relied on manipulating material
properties to match complex experiments. Our model uses the Stefan problem with
a density jump to provide a straightforward method for validating multiphysics
simulations involving heat sources and phase changes in three-phase
flows.Lastly, we demonstrate the practical utility of the method in modeling
porosity defects (gas bubble trapping) during metal solidification. A field
extension technique is used to accurately apply surface tension forces in a
three-phase flow situation. This is where part of the bubble surface is trapped
within the (moving) solidification front.
