An inverse model for a free-boundary problem with a contact line: Steady case
- Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4K1 (Canada)
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.
- OSTI ID:
- 21308095
- Journal Information:
- Journal of Computational Physics, Vol. 228, Issue 13; Other Information: DOI: 10.1016/j.jcp.2009.03.042; PII: S0021-9991(09)00173-9; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model
Solution of one- and two-phase melting and solidification problems imposed with constant or time-variant temperature and flux boundary conditions