Inverse Design of Time Dependent Solidification Processes

An inverse algorithm is developed for the design of the solidification processing systems. The algorithm entails the use of the Tikhonov regularization method, along with an appropriately selected regularization parameter. Both the direct solution of moving boundary problems and the inverse design formulation are presented, along with the L-curve method to select an optimal regularization parameter for inverse design calculations. The design algorithm is applied to determine the optimal boundary heat flux distribution in order to obtain a unidirectional solidification front moving at a constant velocity in a 2-D cavity by eliminating the effect of natural convection. The inverse calculation is also performed for the case in which the solid-liquid interface is prescribed to vary with sine functions. The L-curve based regularization method is found to be reasonably accurate for the purpose of designing time dependent solidification processing systems.