“…( 1)-(3) require a closure relation, which is given, depending on the application, either by an equation of state, or by discrete curves determined by experiments. In each case, we have a relation ρ = ρ(T, p), with the temperature and pressure both being functions of space x and time t. In many boiling simulations in literature, an assumption of the incompressibility of the vapor phase is often imposed (example, [10,31,50]), to focus on the modelling of the phase transition process itself. Here, we allow the possibility of both incompressible and compressible vapor phases, by using different closure relations.…”