A rapidly converging phase field model

Xinfu Chen; G. Caginalp; Christof Eck

doi:10.3934/dcds.2006.15.1017

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2006, Volume 15, Issue 4: 1017-1034. Doi: 10.3934/dcds.2006.15.1017

This issue Previous Article Introduction Next Article Phase-field modelling of nonequilibrium partitioning during rapid solidification in a non-dilute binary alloy

A rapidly converging phase field model

1.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
2.
Institute of Applied Mathematics, University Erlangen-Nurenberg 91058 Erlangen

Received: November 30, 2004

Published: September 2006

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Abstract

We propose a phase field model that approximates its limiting sharp interface model (free boundary problem) up to second order in interface thickness. A broad range of double-well potentials can be utilized so long as the dynamical coefficient in the phase equation is adjusted appropriately. This model thereby assures that computation with particular value of interface thickness $\varepsilon$, will differ at most by $O(\varepsilon^2$) from the limiting sharp interface problem. As an illustration, the speed of a traveling wave of the phase field model is asymptotically expanded to demonstrate that it differs from the speed of the traveling wave of the limit problem by $O(\varepsilon^2)$.

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Mathematics Subject Classification: Primary: 80A22, 80M35; Secondary: 35K55.

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