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Numerical computation of advection and diffusion on evolving diffuse interfaces
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Elliott, Charles M., Stinner, Björn, Styles, Vanessa and Welford, R. (2011) Numerical computation of advection and diffusion on evolving diffuse interfaces. IMA Journal of Numerical Analysis, Vol.31 (No.3). pp. 786-812. doi:10.1093/imanum/drq005 ISSN 0272-4979.
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Official URL: http://dx.doi.org/10.1093/imanum/drq005
Abstract
We propose a numerical method for computing transport and diffusion on a moving surface. The approach is based on a diffuse interface model in which a bulk diffusion-advection equation is solved on a layer of thickness epsilon containing the surface. The conserved quantity in the bulk domain is the concentration weighted by a density which vanishes on the boundary of the thin domain. Such a density arises naturally in double obstacle phase field models. The discrete equations are then formulated on a moving narrow band consisting of grid points on a fixed mesh. We show that the discrete equations are solvable subject to a natural constraint on the evolution of the discrete narrow band. Mass is conserved and the discrete solution satisfies stability bounds. Numerical experiments indicate that the method is second-order accurate in space.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Differential equations, Partial -- Numerical solutions -- Computer programs, Interfaces (Physical sciences) -- Mathematics , Heat equation, Finite element method, Surface active agents | ||||
Journal or Publication Title: | IMA Journal of Numerical Analysis | ||||
Publisher: | Oxford University Press | ||||
ISSN: | 0272-4979 | ||||
Official Date: | July 2011 | ||||
Dates: |
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Volume: | Vol.31 | ||||
Number: | No.3 | ||||
Page Range: | pp. 786-812 | ||||
DOI: | 10.1093/imanum/drq005 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Deutsche Forschungsgemeinschaft (DFG), Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | Sti 579/1-1 2 (DFG), EP/D078334/1 (EPSRC), EP/G010404 (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
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