Solving two typical inverse Stefan problems by using the Lie-group shooting method
Resource
International Journal of Heat and Mass Transfer, 54(9-10), 1941-1949
Journal
International Journal of Heat and Mass Transfer
Pages
1941-1949
Date Issued
2011
Date
2011
Author(s)
Liu, Chein-Shan
Abstract
We consider two typical inverse Stefan problems: one is computing a heat flux boundary condition when the moving boundary ξ(t) is given, and another is recovering an unknown moving boundary ξ(t), by knowing an extra Dirichlet boundary condition on the accessible boundary. Through a domain embedding method, we can transform the inverse problem into a parameter identification problem of an advection-diffusion partial differential equation, where ξ(t) and ξ̇(t) play the role of unknown parameters for the second inverse problem. The ξ̇(t) appeared in the governing equation makes the identification of ξ(t) rather difficult. However, upon using the Lie-group shooting method (LGSM) we can derive a simple system of algebraic equations to iteratively calculate ξ̇(t) and then ξ(t) at some discretized times. It is demonstrated through numerical examples that the LGSM is accurate and stable, although under a large measurement noise. © 2011 Elsevier Ltd. All rights reserved.
Type
journal article
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