Computation of the relative diffusivity of porous materials from their microstructure

in preparation, June, 2007

Authors

• Andreas Wiegmann
• Aivars Zemitis

Abstract

"The homogenization approch to finding the relative diffusivity of a porous media is to solve the Poisson problem with appropriate boundary conditions on the pore walls. These Poisson problems are solved by extending the equation also inside the solid portions of the computational domain and viewing the original boundaries as interfaces, with appropriate interface conditions to ensure the solution of the original problem. A Schur-complement formulation for unknown jumps on the interface is derived and solved by the BiCGStab method. Few BiCGStab iterations are needed to solve this complement which suggests that the formulation is rather well-conditioned.<br>The formulation turns out to be the high contrast limit of the computation of the effective thermal conductivity and inherit many of its features. Large scale problems can be solved rapidly with small memory requirements due to the use of an FFT-based Fast Poisson solver. The speed and robustness of the approch make it applicable for virtual material design. Automatic grid generation can be done rapidly and robustly. Low accuracy requirements can be taken advantage of by stopping after few iterations. This technology allows to consider geometris with more than 150 million points in space that can represent relevant porous materials quite well. For an industrial medium, the relative diffusivity is estimated from the porous geometrie."

BibTeX

 
@Article{ Wiegmann.Zemitis06averagingSolver, 
   title = { Computation of the relative diffusivity of porous materials from their microstructure }, 
   author = { Andreas Wiegmann and Aivars Zemitis },               
   note = { in preparation }, 
   month = jun, 
   year = 2007, 
} 

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This publication belongs to the project MultiFil.