An accurate finite-difference method for ablation-type Stefan problems. (English) Zbl 1247.65119

Mitchell, S. L.; Vynnycky, M.

J. Comput. Appl. Math. 236, No. 17, 4181-4192 (2012).

Summary: A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is extended for the purpose of solving one-phase ablation-type moving boundary problems; 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 in order to preserve second-order accuracy in both time and space. The analysis also determines that the ablation front initially moves as the time raised to the power 3/2; hence, it evolves considerably more slowly than the phase-change front in the classical Stefan problem with isothermal cooling.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M32	Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35K05	Heat equation
35R37	Moving boundary problems for PDEs
80A22	Stefan problems, phase changes, etc.
80M20	Finite difference methods applied to problems in thermodynamics and heat transfer

Keywords:

ablation; Stefan problem; Keller box scheme; boundary immobilization; starting solutions; heat equation; numerical examples; algorithm; moving boundary problem; finite-difference scheme; isothermal cooling

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