Time-Dependent Reaction Coefficient Identification Problems with a Free Boundary

Huntul, M. J.; Lesnic, D.

doi:10.1080/15502287.2019.1568619

Cited by 7 publications

(5 citation statements)

References 21 publications

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“…Free boundary problems for parabolic partial differential equations have significant applications in various fields of engineering, physics, chemistry, see [1,3,[7][8][9][10]12,14] to mention only a few. In particular, the Stefan problem is a moving free boundary problem that concerns the distribution of heat in a phase-change transforming medium.…”

Section: Introductionmentioning

confidence: 99%

“…Chen and Feldman (2015) recast the formulation of various shock diffraction/reflection problems as a free boundary problem. Recently, the authors numerically solved several inverse thermal problems concerning the determination of time-dependent coefficients along with free boundaries (Huntul and Lesnic, 2017;Huntul and Lesnic, 2019b;Hussein et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

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Determination of the time-dependent convection coefficient in two-dimensional free boundary problems

Huntul

Lesnic

2021

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Determination of the time-dependent convection coefficient in two-dimensional free boundary problems

Huntul

Lesnic

2021

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“…The free boundary problems for parabolic partial differential equations involving Stefan condition have significant applications in various fields of engineering, physics, chemistry, etc (Broadbridge et al , 1993; Johansson et al , 2011; Hussein and Lesnic, 2014; Chen and Feldman, 2015; Hussein et al , 2016; Huntul and Lesnic, 2017; Huntul and Lesnic, 2019a; Huntul and Lesnic, 2019b). A Stefan problem is a moving boundary value problem that concerns the distribution of heat in a period of transforming medium.…”

Section: Introductionmentioning

confidence: 99%

“…Chen and Feldman (2015) showed the formulation of various shock diffraction/reflection problems as free boundary problems. Recently, authors of Huntul and Lesnic (2017, 2019a) numerically solved heat and inverse heat problems of determining the time-dependent coefficients with free boundaries and time-dependent reaction with free boundary respectively together with Stefan condition, as well as heat moments. Hussein and Lesnic (2014) considered the inverse heat problem of timewise coefficient and free boundary while Hussein et al (2016) investigated multiple timewise terms in inverse heat problems with an unknown free boundary together with Stefan boundary condition and various order heat moments.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Huntul and Lesnic (2019a) investigated the identification of multiple timewise terms along with one side unknown free boundary of the finite slab x ∈ (0, h (t)). In this paper, we investigate the determination of timewise terms, as well as the lower order term b (t) in heat equation along with two-sided unknown free boundaries of the finite slab x ∈ ( h 1 (t), h 2 (t)).…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous identification of timewise terms and free boundaries for the heat equation

Huntul

Tamsir

2020

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Purpose The purpose of this paper is to provide an insight and to solve numerically the identification of timewise terms and free boundaries coefficient appearing in the heat equation from over-determination conditions. Design/methodology/approach The formulated coefficient identification problem is inverse and ill-posed, and therefore, to obtain a stable solution, a nonlinear Tikhonov regularization least-squares approach is used. For the numerical discretization, the finite difference method combined with a regularized nonlinear minimization is performed using the MATLAB subroutine lsqnonlin. Findings The numerical results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data. Research limitations/implications The mathematical formulation is restricted to identify coefficients in unknown components dependent on time, and this may be considered as a research limitation. However, there is no research implication to overcome this, as the known input data is also limited to single temperature in heat equation with Stefan conditions, and the first- and second-order heat moments measurements at a particular time location. Practical implications As noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise. Social implications The identification of the timewise terms and free boundaries will be of great interest in the heat transfer community and related fluid flow applications. Originality/value The current investigation advances previous studies, which assumed that the coefficient multiplying the lower order temperature term depends on time. The knowledge of this physical property coefficient is very important in heat transfer and fluid flow. The originality lies in the insight gained by performing for the numerical simulations of inversion to find the timewise terms and free boundaries coefficient dependent on time in the heat equation from noisy measurements.

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A numerical investigation of unsteady space–time dependent coefficients anisotropic-diffusion convection reaction equation

Azis

2023

Engineering Analysis with Boundary Elements

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Time-Dependent Reaction Coefficient Identification Problems with a Free Boundary

Cited by 7 publications

References 21 publications

Determination of the time-dependent convection coefficient in two-dimensional free boundary problems

Determination of the time-dependent convection coefficient in two-dimensional free boundary problems

Simultaneous identification of timewise terms and free boundaries for the heat equation

A numerical investigation of unsteady space–time dependent coefficients anisotropic-diffusion convection reaction equation

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