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An explicit unconditionally stable variable time‐step method for one‐dimensional stefan problems
Author(s) -
Zerroukat M.,
Chatwin C. R.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620350708
Subject(s) - variable (mathematics) , convergence (economics) , mathematics , stability (learning theory) , boundary (topology) , boundary value problem , finite difference method , mathematical optimization , mathematical analysis , computer science , machine learning , economics , economic growth
Modelling of heat conduction processes with phase changes benefits from the application of variable time‐step methods when the behaviour of the moving boundary is not known a prioiri . Due to convergence and stability constraints only implicit difference equations have been used with these methods. Implicit methods show a significant loss of accuracy and exhibit convergence difficulties when used for relatively slow or rapid moving‐boundary problems. To overcome these problems an improved explicit variable time‐step method which combines the explicit exponential difference equation and a variable time‐step grid network with virtual subspace increments around the moving boundary is presented and tested for both a solidification and a melting problem. A virtual subinterval time‐step elimination technique is incorporated to ensure that stability is automatically maintained for any mesh size. Unlike the implicit variable time‐step methods, the accuracy of the resulting method is not affected by the velocity of the moving boundary. For both test problems numerical results are in better agreement with known analytical solutions than results predicted by other numerical methods.