A transient three-dimensional inverse geometry problem in estimating the space and time-dependent irregular boundary shapes

A transient three-dimensional shape identification problem (inverse geometry problem) to determine the unknown irregular and moving boundary configurations by utilizing the steepest descend method (SDM) and a general purpose commercial code CFD-RC is successfully developed and examined in this study based on the simulated measured temperature distributions on the bottom surface by infrared thermography. The advantage of calling CFD-RC as a subroutine in the present inverse calculation lies in that its auto-mesh function enables the handling of this moving boundary problem. Results obtained by using the technique of SDM to solve the inverse geometry problem are justified based on the numerical experiments. Two test cases are performed to test the validity of the present algorithm by using different types of boundary shapes, initial guesses and measurement errors. Results show that reliable estimations on the unknown space and time-dependent boundary geometry can be obtained when the measurement errors are considered.