FFT-based bounds on the permeability of complex microstructures

François Bignonnet (1) , Luc Dormieux (1)

1 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes

A numerical scheme for the computation of the permeability of complex microstructures is presented. As a darcean counterpart of the FFT-based scheme in elasticity, the method is designed to be directly coupled with 3D imaging techniques of porous samples, without meshing or definition of an equivalent pore network. The method relies on the variational principle of Hashin and Shtrikman which ensures a rigorous upper bound status to the estimated permeabilities and provides an energetically consistent rule for heterogeneous voxels comprising both the solid and fluid phases.

Keywords: Permeability; Numerical homogenization; Fast Fourier Transform; Variational framework; Polarization

Domains: Mechanics [physics.med-ph]; Mechanics of materials [physics.class-ph]; Fluid mechanics [physics.class-ph]

François Bignonnet, Luc Dormieux. FFT-based bounds on the permeability of complex microstructures. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38, pp.1707 - 1723. ⟨10.1002/nag.2278⟩. ⟨hal-01084229⟩