The oxygen diffusion problem: Analysis and numerical solution

S. L. Mitchell; M. Vynnycky

doi:10.1016/j.apm.2014.10.068

The oxygen diffusion problem: Analysis and numerical solution

S. L. Mitchell
, M. Vynnycky

KTH Royal Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is applied to the classical moving boundary problem that arises from the diffusion of oxygen in absorbing tissue; in tandem with the Keller box finite-difference scheme, the so-called boundary immobilization method is used. New insights are obtained into three aspects of the problem: the numerical accuracy of the scheme used; the calculation of oxygen depletion time; and the behaviour of the moving boundary as the oxygen is depleted.

Original language	English
Pages (from-to)	2763-2776
Number of pages	14
Journal	Applied Mathematical Modelling
Volume	39
Issue number	9
DOIs	https://doi.org/10.1016/j.apm.2014.10.068
Publication status	Published - 1 May 2015

Keywords

Depletion time
Keller box scheme
Moving boundary
Oxygen diffusion

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10.1016/j.apm.2014.10.068

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abstract = "A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is applied to the classical moving boundary problem that arises from the diffusion of oxygen in absorbing tissue; in tandem with the Keller box finite-difference scheme, the so-called boundary immobilization method is used. New insights are obtained into three aspects of the problem: the numerical accuracy of the scheme used; the calculation of oxygen depletion time; and the behaviour of the moving boundary as the oxygen is depleted.",

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N2 - A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is applied to the classical moving boundary problem that arises from the diffusion of oxygen in absorbing tissue; in tandem with the Keller box finite-difference scheme, the so-called boundary immobilization method is used. New insights are obtained into three aspects of the problem: the numerical accuracy of the scheme used; the calculation of oxygen depletion time; and the behaviour of the moving boundary as the oxygen is depleted.

AB - A recently derived numerical algorithm for one-dimensional time-dependent Stefan problems is applied to the classical moving boundary problem that arises from the diffusion of oxygen in absorbing tissue; in tandem with the Keller box finite-difference scheme, the so-called boundary immobilization method is used. New insights are obtained into three aspects of the problem: the numerical accuracy of the scheme used; the calculation of oxygen depletion time; and the behaviour of the moving boundary as the oxygen is depleted.

KW - Depletion time

KW - Keller box scheme

KW - Moving boundary

KW - Oxygen diffusion

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The oxygen diffusion problem: Analysis and numerical solution

Abstract

Keywords

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