Determination of the time-dependent convection coefficient in two-dimensional free boundary problems. Issue 10 (6th May 2021)

• Record Type: Journal Article
• Authors: Huntul, Mousa; Lesnic, Daniel
• Is Part Of: Engineering computations. Volume 38:Issue 10(2021)
• Page Start: 3694
• Page End: 3709
• Publication Date: 2021-05-06
• Subjects: Inverse problem -- Nonlinear optimization -- Tikhonov regularization -- Free boundary -- Two-dimensional -- heat equation; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-10-2020-0562
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of the study is to solve numerically the inverse problem of determining the time-dependent convection coefficient and the free boundary, along with the temperature in the two-dimensional convection-diffusion equation with initial and boundary conditions supplemented by non-local integral observations. From the literature, there is already known that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. Design/methodology: For the numerical discretization, this paper applies the alternating direction explicit finite-difference method along with the Tikhonov regularization to find a stable and accurate numerical solution. The resulting nonlinear minimization problem is solved computationally using the MATLAB routine lsqnonlin. Both exact and numerically simulated noisy input data are inverted. Findings: The numerical results demonstrate that accurate and stable solutions are obtained. Originality/value: The inverse problem presented in this paper was already showed to be locally uniquely solvable, but no numerical solution has been realized so far; hence, the main originality of this work is to attempt this task.