A regularization method for the inverse design of solidification processes with natural convection

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 the L-curve method to select an optimal regularization parameter. Both the direct solution of moving boundary problems and the inverse design formulation are presented. The design algorithm is applied to determine the optimal boundary heat flux distribution to obtain a unidirectional solid-liquid interface in a 2-D cavity. The inverse calculation is also performed with a prescribed sinuous solid-liquid interface. To this end, a whole time-domain method and a sequential method are used and evaluated. The L-curve based regularization method is found to be reasonably accurate for the purpose of designing solidification processing systems. We also found that the sequential method with appropriately selected time domains is comparative to the whole time-domain method.