A singular-perturbed two-phase Stefan problem
โ Scribed by J. Struckmeier; A. Unterreiter
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 266 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0893-9659
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โฆ Synopsis
The asymptotic behavior of a singular-perturbed two-phase Stefan problem due to slow diffusion in one of the two phases is investigated. In the limit, the model equations reduce to a one-phase Stefan problem. A boundary layer at the moving interface makes it necessary to use a corrected interface condition obtained from matched asymptotic expansions. The approach is validated by numerical experiments using a front-tracking method.
๐ SIMILAR VOLUMES
Both one-dimensional two-phase Stefan problem with the thermodynamic equilibrium condition uรฐRรฐtร; tร ยผ 0 and with the kinetic rule u e รฐR e รฐtร; tร ยผ eR 0 e รฐtร at the moving boundary are considered. We prove, when e approaches zero, R e รฐtร converges to Rรฐtร in C 1รพd=2 ยฝ0; T for any finite T > 0;
It is well known that the classical two-phase Stefan problem, which is an orderpreserving system, can be regarded as a singular limit of a phase field model. However the rigorous analysis of the phase field model is not easy, because it is not an order-preserving system and also is strongly coupled.