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Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Adams, Matthew P., Mallet, Daniel G., & Pettet, Graeme J. (2012) Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes. In Gu, YuanTong & Saha, Suvash C. (Eds.) Proceedings of 4th International Conference on Computational Methods (ICCM2012), Gold Coast, Qld. (In Press)

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Abstract

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

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ID Code: 53470
Item Type: Conference Paper
Keywords: Growing domain, Nonuniform growth, Continuum, Epithelium, Skin substitute
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Biological Mathematics (010202)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > Institutes > Institute of Health and Biomedical Innovation
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2012 please consult the authors
Deposited On: 06 Sep 2012 13:20
Last Modified: 25 Feb 2013 14:35

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