On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions

• Autores: Susan L. Mitchell, M. Vynnycky
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 264, Nº 1, 2014, págs. 49-64
• Idioma: inglés
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• Resumen

  • A recently derived numerical algorithm for one-dimensional one-phase Stefan problems is extended for the purpose of two-phase moving boundary problems in which the second phase first appears only after a finite delay time; this can occur if the phase change is caused by a heat-flux boundary condition. In tandem with the Keller box finite-difference scheme, the so-called boundary immobilization method is used. An important component of the work is the use of variable transformations that must be built into the numerical algorithm to resolve the boundary-condition discontinuity that is associated with the onset of phase change. This allows the delay time until solidification begins to be determined, and gives second-order accuracy in both time and space.