A multi‐level adaptive solution strategy for 3D inverse problems in pool boiling

Abstract

PurposeThe purpose of this paper is to present an efficient algorithm based on a multi‐level adaptive mesh refinement strategy for the solution of ill‐posed inverse heat conduction problems arising in pool boiling using few temperature observations.Design/methodology/approachThe stable solution of the inverse problem is obtained by applying the conjugate gradient method for the normal equation method together with a discrepancy stopping rule. The resulting three‐dimensional direct, adjoin and sensitivity problems are solved numerically by a space‐time finite element method. A multi‐level computational approach, which uses an a posteriori error estimator to adaptively refine the meshes on different levels, is proposed to speed up the entire inverse solution procedure.FindingsThis systematic approach can efficiently solve the large‐scale inverse problem considered without losing necessary detail in the estimated quantities. It is shown that the choice of different termination parameters in the discrepancy stopping conditions for each level is crucial for obtaining a good overall estimation quality. The proposed algorithm has also been applied to real experimental data in pool boiling. It shows high computational efficiency and good estimation quality.Originality/valueThe high efficiency of the approach presented in the paper allows the fast processing of experimental data at many operating conditions along the entire boiling curve, which has been considered previously as computationally intractable. The present study is the authors' first step towards a systematic approach to consider an adaptive mesh refinement for the solution of large‐scale inverse boiling problems.

A new operational matrix method based on the Bernstein polynomials for solving the backward inverse heat conduction problems

“…Regularization methods are most powerful and efficient methods for ill-posed problems (Tikhonov and Arsenin, 1977;Ira and Galybin, 2011). In our computation we use Tikhonov regularization method (Heng et al, 2011;Mera et al, 2003;Dousti et al, 2012) to solve the matrix equation arising from the presented method. Other regularization method such as truncated singular value decomposition and conjugate gradient methods, could be considered.…”