Abstract
A new formulation possessing stable numerical characteristics is presented for inverse Stefan design processes. In such processes, the goal of the analysis is to design transient boundary conditions which produce the desired interfacial surface motion. This subclass of mildly ill-posed mathematical problems is amenable to the proposed solution methodology. This investigation presents a fixed-front differential formulation from which a weighted residual statement is developed. Orthogonal collocation is used to obtain numerical results illustrating the merit of imposing physical constraints in the mathematical model. These mathematical constraints can be viewed as design specifications and are available to the designer or experimentalist. The proposed methodology is flexible and can be generalized to problems involving continuous casting or crystal growth. Finally, symbolic manipulation is used for augmenting the computational methodology.
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Frankel, J.I. Constraining inverse stefan design problems. Z. angew. Math. Phys. 47, 456–466 (1996). https://doi.org/10.1007/BF00916649
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DOI: https://doi.org/10.1007/BF00916649