Mathematical analysis of phase-field equations with numerically efficient coupling terms

Abstract

This paper deals with the equations in a phase-field model with special terms coupling the heat equation and the equation of phase. A finer control of latent heat release together with a gradient coupling term in the phase equation are introduced as a consequence of an extensive numerical work with models of phase transitions within the context of the solidification of crystalline substances. We present a proof of the existence and uniqueness of the weak solution of the modified system of equations. Furthermore, we perform an asymptotic procedure to recover sharp-interface relations. Finally, several numerical studies demonstrate how the model behaves compared to its standard version.