The macroscale boundary conditions for diffusion in a material with microscale varying diffusivities

@article{Chen2014TheMB,
  title={The macroscale boundary conditions for diffusion in a material with microscale varying diffusivities},
  author={Chen Chen and Anthony J. Roberts and Judith Bunder},
  journal={Anziam Journal},
  year={2014},
  volume={55},
  pages={218-234}
}
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… 

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  • 2014