Predictive entropy based correction of phase change computations with fluid flow - Part 1: Second law formulation

A numerical formulation involving the Second Law of Thermodynamics is exami ned in the analysis of phase change problems with fluid flow. The discretiz ed entropy transport equation and entropy boundary conditions are described for solid-liquid systems. In addition, the downward concavity and compatib ility properties of entropy are applied in a discrete entropy based stabili ty analysis. Discrete analogies of the Second Law provide a physical basis for nonlinear phase-temperature iterations in the energy equation. The nume rical formulation includes both corrective steps for accuracy improvements (entropy based diffusivity) as well as predictive steps (entropy based time constraint) for stable computations. It is anticipated that this Second La w formulation can provide an effective enhancement for accurate simulations in phase change problems with fluid flow.