On the numerical solution of a Stefan problem with finite extinction time

• M. Vynnycky ^[1] ; S.L. Mitchell ^[2]
  1. [1] Royal Institute of Technology

     Royal Institute of Technology

     Suecia

     
  2. [2] University of Limerick

     University of Limerick

     Irlanda

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 276, Nº 1 (1 March 2015), 2015, págs. 98-109
• Idioma: inglés
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• Resumen

  • In many phase-change problems of practical interest, it is important to know when a phase is depleted, a quantity referred to as the extinction time; however, there are no numerical schemes that are able to compute this with any degree of rigour or formal accuracy. In this paper, we develop such a scheme for the one-dimensional time-dependent problem of an evaporating spherical droplet. The Keller box finite-difference scheme is used, in tandem with the so-called boundary immobilization method. An important component of the work is the careful use of variable transformations that must be built into the numerical algorithm in order to preserve second-order accuracy in both time and space, in particular as regards resolving a square-root singularity in the droplet radius as the extinction time is approached.