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Coupled reaction-diffusion systems and evolving microstructure: mathematical modelling and homogenisation

Malte Andreas Peter

ISBN 978-3-8325-1503-4
170 pages, year of publication: 2007
price: 40.50 €
Chemical processes in porous media are modelled on the pore scale using reaction-diffusion equations. The resulting prototypical systems of coupled linear and nonlinear differential equations are homogenised in the context of periodic media. Particular attention is paid to the scaling of certain terms of the reaction-diffusion system with powers of the homogenisation parameter and the accounting for an evolution of the microstructure. Numerical simulations confirm the appropriateness of the resulting macroscopic limit problems. Moreover, simulations for the real-world problem of concrete carbonation are performed showing that the accounting for the evolution of the microstructure leads to a better approximation of experimental data.

Keywords:
  • periodic homogenization
  • reaction-diffusion
  • nonlinear parabolic systems
  • porous media
  • multi-scale

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40.50 €