Mathematical analysis of phase-field equations with numerically efficient coupling terms
Michal Beneš
Charles University, Praha, Czech Republic
![Mathematical analysis of phase-field equations with numerically efficient coupling terms cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-ifb-volume-3-issue-2.png&w=3840&q=90)
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.
Cite this article
Michal Beneš, Mathematical analysis of phase-field equations with numerically efficient coupling terms. Interfaces Free Bound. 3 (2001), no. 2, pp. 201–212
DOI 10.4171/IFB/38