Structured Multiblock Body-Fitted Grids Solution of Transient Inverse Heat Conduction Problems in an Arbitrary Geometry

Abstract

The aim of this study is to develop iterative regularization algorithms based on parameter and function estimation techniques to solve two-dimensional/axisymmetric transient inverse heat conduction problems in curvilinear coordinate system. The multiblock method is used for geometric decomposition of the physical domain into regions with patched-overlapped interface grids. The central finite-difference version of the alternating-direction implicit technique together with structured body-fitted grids is implemented for numerical solution of the direct problem and other partial differential equations derived by inverse analysis. The approach of estimating unknown parameters and functions is iterative inverse analysis algorithms based on the Levenberg-Marquardt method and conjugate gradient methods. The temperature histories are delivered by noisy/non-noisy sensors located on the lower boundary of the domain. Three cases are considered, (1) a time-space-varying upper boundary condition, (2) two time-varying heat sources, and (3) a time-varying heat source and a time-space-varying boundary condition, within a two-dimensional/axisymmetric solid body of arbitrary geometry. The simultaneous estimation of two unknown functions is performed to assess the performance of inverse analysis methods to solve complicated inverse heat conduction problems. The results of the present study are compared to those of exact heat sources and boundary condition, and good agreement is achieved. However, the results show that the accuracy of the upper boundary condition identification is dependent on the uncertainty of the measured temperature data, the number of grid points, and the curvature of the geometric configuration as well.