A two-dimensional inverse heat conduction problem to determine the interfacial configuration of a multiple region domain is solved by utilizing temperature readings on the outer surface of the whole domain. The method used is the modified one-dimensional correction method (MODCM) along with the finite element method. The MODCM is a simple but very accurate method, which first solves the multidimensional inverse heat conduction problem based on the simplified one-dimensional model, and the discrepancy in the result caused by this one-dimensional simplification is corrected afterward by an iterative process. A series of numerical experiments is conducted in order to verify the effectiveness of the algorithm. The method can identify the interfacial configuration of the multiple region domain with high accuracy. The average relative error of the identification result is not more than 10.4% when the standard deviation of the temperature measurement is less than 2.0% of the average measured temperature for the cases tested. The number of the measurement points of the inspection surface can be reduced with no obvious effect on the estimation results as long as it is still sufficient to describe the exact interfacial configuration. The method is proved to be a simple, fast, and accurate one that can solve successfully this interfacial configuration identification problem.
Application of meshless local radial point interpolation (MLRPI) on a one-dimensional inverse heat conduction problem
