کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
521566 | 867775 | 2009 | 18 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: An inverse model for a free-boundary problem with a contact line: Steady case An inverse model for a free-boundary problem with a contact line: Steady case](/preview/png/521566.png)
This paper reformulates the two-phase solidification problem (i.e., the Stefan problem) as an inverse problem in which a cost functional is minimized with respect to the position of the interface and subject to PDE constraints. An advantage of this formulation is that it allows for a thermodynamically consistent treatment of the interface conditions in the presence of a contact point involving a third phase. It is argued that such an approach in fact represents a closure model for the original system and some of its key properties are investigated. We describe an efficient iterative solution method for the Stefan problem formulated in this way which uses shape differentiation and adjoint equations to determine the gradient of the cost functional. Performance of the proposed approach is illustrated with sample computations concerning 2D steady solidification phenomena.
Journal: Journal of Computational Physics - Volume 228, Issue 13, 20 July 2009, Pages 4893–4910