The numeric solution of a modified Stefan problem in the presence of a generalized kinetic undercooling term is investigated. Two fixed-grid methods and a deforming-grid scheme are described. The fixed-grid phase-field method is extended to encompass a generalized dependence of the melting temperature on the front velocity. Two liquid fraction-based methods are also provided, which are discretized over a deforming grid and a fixed grid, respectively. Results show that, whereas the deforming-grid scheme is the most efficient for one-dimensional problems, the phase-field method is a competitive choice among fixed-grid schemes.
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Received 4 January 1994; accepted 12 November 1994. M. Fabbri would like to acknowledge a scholarship from the Conselho Nacional de Desenvolvi-mento Cientifico e Technologico, CNPq, Brazil. This work was also supported by a resource grant from the Minnesota Supercomputer Institute, Minneapolis, MN, USA. Address correspondence to Dr. Vaughan R. Voller, Department of Civil Engineering, University of Minnesota, 122 Civil and Mineral Engineering Building, 500 Pillsbury Drive S. E., Minneapolis, MN 554550220. USA.