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Macroscale modelling of multilayer diffusion: Using volume averaging to correct the boundary conditions

Abstract : This paper investigates the form of the boundary conditions (BCs) used in macroscale models of PDEs with coefficients that vary over a small length-scale (microscale). Specifically, we focus on the one-dimensional multilayer diffusion problem, a simple prototype problem where an analytical solution is available. For a given microscale BC (e.g., Dirichlet, Neumann, Robin, etc.) we derive a corrected macroscale BC using the method of volume averaging. For example, our analysis confirms that a Robin BC should be applied on the macroscale if a Dirichlet BC is specified on the microscale. The macroscale field computed using the corrected BCs more accurately captures the averaged microscale field and leads to a reconstructed microscale field that is in excellent agreement with the true.microscale field. While the analysis and results are presented for one-dimensional multilayer diffusion only, the methodology can be extended to and has implications on a broader class of problems.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01652588
Contributor : Catherine Kruch Connect in order to contact the contributor
Submitted on : Thursday, November 30, 2017 - 2:23:05 PM
Last modification on : Tuesday, July 20, 2021 - 3:06:17 AM

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E.J. Carr, I.W. Turner, Patrick Perre. Macroscale modelling of multilayer diffusion: Using volume averaging to correct the boundary conditions. Applied Mathematical Modelling, Elsevier, 2017, 47, pp.600 - 618. ⟨10.1016/j.apm.2017.03.044⟩. ⟨hal-01652588⟩

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