A three-dimensional inverse geometry problem in estimating the space and time-dependent shape of an irregular internal cavity

A three-dimensional inverse geometry problem (or shape identification problem) to estimate the unknown space and time-dependent irregular shape of internal cavity by utilizing the gradient-based steepest descent method (SDM) and a general purpose commercial code CFD-ACE+ is considered in the present study. The validity of the present inverse algorithm is examined based on the simulated measured temperature distributions on the outer surface by an imaginary infrared scanner. The advantage of calling CFD-ACE+ as a subroutine in this shape identification problem lies in its characteristics of automatic mesh generation since this function of CFD-ACE+ enables the easily-handling of the moving boundary problem. Two numerical test cases are performed to test the validity and accuracy of the present shape identification algorithm by using different types of cavity shapes, initial guesses and measurement errors. Results show that excellent estimations on the unknown geometry of the internal cavity can be obtained.