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Esen, A.; Kutluay, S.

A numerical solution of the Stefan problem with a Neumann-type boundary condition by enthalpy method. (English) Zbl 1034.65070

Appl. Math. Comput. 148, No. 2, 321-329 (2004).
Summary: The enthalpy method based on suitable finite difference approximations has been applied to the one-dimensional moving boundary problem with a Neumann-type boundary condition known as the Stefan problem. The numerical results obtained by the hopscotch technique are compared with the exact solution of the problem. It is shown that all results are found to be in very good agreement with each other, and the numerical solution displays the expected convergence to the exact one as the mesh size is refined.

Cited in 15 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

Enthalpy method; Stefan problem; Hopscotch technique; finite difference; moving boundary problem; convergence; numerical examples

Software:

Hopscotch
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Full Text: DOI

References:

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