Comparison of Asymptotic Solutions of Phase-Field Models to
a Sharp-Interface Model

By Dr. S.I. Hariharan

Division of Applied Mathematics
The University of Akron
Akron, Ohio 44325


A one-dimensional, quasi-steady, directional solidification problem is considered for the purpose of analyzing the relationship between the solution resulting from a phase-field model to that from a sharp-interface model whose exact solution is known. In the phase-field case, the quasi-steady approximation is coupled with a small-interface thickness boundary-layer expansion. By tuning the kinetic parameter, we develop phase-field temperature profiles that agree with the sharp-interface profiles, except near the solidification front, where there is smoothing over the diffuse interface and no jump in the temperature gradients. This results in agreement between the locations of the sharp-interface and phase-field solidification fronts.

To Be Presented At The

3rd Forum On Numerics & Modeling for
Partial Differential Equations

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