A Hyperbolic Phase-Field Approach for Solidification with Supercooling

Yuqi Chen, James M. McDonough, Kaveh A. Tagavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This report concerns the solidification of a “supercooled” liquid, whose temperature is initially below the equilibrium melt temperature, Tm of the solid. A new approach, the phase-field method, will be applied for this Stefan problem with supercooling, which simulates the solidification process of a pure material into a supercooled liquid in a spherical region. The advantage of the phase-field method is that it bypasses explicitly tracking the freezing front. In this approach the solid-liquid interface is treated as diffuse, and a dynamic equation for the phase variable is introduced in addition to the equation for heat flow. Thus, there are two coupled partial differential equations for temperature and phase held. In the reported study, an implicit numerical scheme using finite-difference techniques on a uniform mesh is employed to solve both Fourier phase-field equations and non-Fourier (known as damped wave or telegraph) phase-field equations. The latter gurantees a finite speed of propagation for the solidification front. Both Fourier (parabolic) and non-Fourier (hyperbolic) Stefan problems with supercooling are satisfactorily simulated and their solutions compared in the present work.

Original languageEnglish
Title of host publicationHeat Transfer
Subtitle of host publicationVolume 2
Number of pages9
ISBN (Electronic)9780791826676
StatePublished - 1999
EventASME 1999 International Mechanical Engineering Congress and Exposition, IMECE 1999 - Nashville, United States
Duration: Nov 14 1999Nov 19 1999

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)


ConferenceASME 1999 International Mechanical Engineering Congress and Exposition, IMECE 1999
Country/TerritoryUnited States

Bibliographical note

Funding Information:
Support of this work by the National Aeronautics and Space Administration (NASA) NASA-EPSCoR Grant WKU 522762-98-03 is gratefully acknowledged.

Publisher Copyright:
© 1999 American Society of Mechanical Engineers (ASME). All rights reserved.

ASJC Scopus subject areas

  • Mechanical Engineering


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