1. On the numerical solution of a Stefan problem with finite extinction time.
- Author
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Vynnycky, M. and Mitchell, S.L.
- Subjects
- *
NUMERICAL analysis , *PROBLEM solving , *SCHEMES (Algebraic geometry) , *FINITE differences , *ALGORITHMS - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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