Fixed Domain and Deforming FEM Techniques as Applied to Some Inverse Solidification Problems

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This research addresses the development and verification of mathematical models for the solution of inverse problems associated with phase change casting processes. The methodology is based on sequential and regularization methods in conjunction with an implicit Finite Element Method (FEM) formulation and deforming FEM techniques. A general analysis of inverse phase change problems including variable material properties will be developed. Casting processing involving mushy regions and complex geometries will be considered. This analytical research is closely tied to an industrial affiliate who is performing the associated experiments. Solidification processes are of vital engineering significance. There is no existing methodology for the computational analysis of inverse phase change problems. This research considers the development of inverse techniques for phase change problems, the control of solidification processes and the associated microstructure is possible. This could lead to significant fundamental and practical contributions of importance to our industrial institutions.