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https://hdl.handle.net/2440/95518
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Type: | Conference paper |
Title: | The macroscale boundary conditions for diffusion in a material with microscale varying diffusivities |
Author: | Chen, C. Roberts, A. Bunder, J. |
Citation: | ANZIAM Journal : Electronic Supplement, 2014 / Roberts, A., Bassom, A., Hocking, G., Nelson, M., Popiel, T., Bunder, J., Borwein, J., Rath, N., AustMS, (ed./s), vol.55, pp.C218-C234 |
Publisher: | Cambridge University Press |
Issue Date: | 2014 |
ISSN: | 1445-8810 |
Conference Name: | 11th Engineering Mathematics and Applications Conference (EMAC2013) (1 Dec 2013 - 4 Dec 2013 : Brisbane, Qld.) |
Editor: | Roberts, A. Bassom, A. Hocking, G. Nelson, M. Popiel, T. Bunder, J. Borwein, J. Rath, N. AustMS, |
Statement of Responsibility: | Chen Chen, Anthony John Roberts, Judith Bunder |
Abstract: | Homogenization and other multiscale modelling techniques empower us to build efficient mathematical models for simulating materials with complicated microstructures. However, the modelling rarely systematically derives boundary conditions for the macroscale models. We build a smooth macroscale model for a two-layer one-dimensional lattice diffusion system with rapidly varying diffusivity and finite scale separation. We derive macroscale boundary conditions for this diffusion problem. Our approach is applicable to a range of multiscale modelling problems including wave equations. |
Keywords: | micro; macro; multiscale; boundary condition; diffusion; centre manifold theory; macroscale modelling |
Rights: | © Copyright Australian Mathematical Society 2014 |
DOI: | 10.21914/anziamj.v55i0.7853 |
Published version: | http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/7853 |
Appears in Collections: | Aurora harvest 3 Education publications |
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