Application of optimization methods for solving inverse phase-change problems

Several optimization algorithms in conjunction with a control-volume method (for discretization) and a least-square method (for improving accuracy and stability) have been considered to solve the inverse phase-change problem for the example of the welding process. The results show that quite an accurate solution can be obtained when the sensors are placed near the interface region. The most important feature of the approach is that the liquid-solid interface as well as the temperature distribution within the solid region can be obtained from the temperature data at a number of sensors located in the solid region, without considering heat transfer and fluid flow in a molten zone. The validity of the numerical solution of the inverse problem is checked by comparing the results with direct solution of the problem. The inverse approach to phase-change problems has many potential applications that are of great technological significance.