CONSTRAINING INVERSE STEFAN DESIGN-PROBLEMS

A new formulation possessing stable numerical characteristics is prese nted for inverse Stefan design processes. In such processes, the goal of the analysis is to design transient boundary conditions which produ ce the desired interfacial surface motion. This subclass of mildly ill -posed mathematical problems is amenable to the proposed solution meth odology. This investigation presents a fixed-front differential formul ation from which a weighted residual statement is developed. Orthogona l collocation is used to obtain numerical results illustrating the mer it of imposing physical constraints in the mathematical model. These m athematical constraints can be viewed as design specifications and are available to the designer or experimentalist. The proposed methodolog y is flexible and can be generalized to problems involving continuous casting or crystal growth. Finally, symbolic manipulation is used for augmenting the computational methodology.