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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.
Statement of
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
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