INVERSE FINITE-ELEMENT REDUCED MESH METHOD FOR PREDICTING MULTIDIMENSIONAL PHASE-CHANGE BOUNDARIES AND NONLINEAR SOLID-PHASE HEAT-TRANSFER

An inverse finite element method is developed for simultaneous solutio n of multi-dimensional solid-liquid phase boundaries and associated th ree-dimensional solid phase temperature fields. The technique, applica ble to quasisteady phase change problems, fixes element nodes at known temperature locations and uses a coarse, spatially limited mesh. This approach is designed to: (1) reduce direct and overall solution costs , (2) eliminate iterative direct solutions associated with temperature dependent thermophysical properties, (3) limit calculations to the he at affected zone and (4) eliminate ad hoc assumptions concerning the b oundary heat flux distribution. The inverse algorithm couples a nonlin ear solid phase conduction solver with conjugate gradient minimization . First-order regularization and upwind differencing are implemented t o improve solution smoothness and stability and an analog welding expe riment is used to investigate the technique's capabilities.