Permeability Computation on a Representative Volume Element (RVE) of Unidirectional Disordered Fiber Arrays (Journal of Computational Mathematics, 2018)
An efficient method to compute the permeability of disordered fibrous arrays is proposed. A stabilized mixed finite element method is used with an immersed domain approach to represent the porous material at its microscopic scale. Therefore, the Stokes equations are solved in the whole domain (including solid part) using a penalization method. The accuracy is controlled by refining the mesh around the fluid-solid interface defined by a level-set function. Using homogenization techniques, the permeability of an RVE is obtained. Furthermore, a new method to generate disordered fibers in function of the porosity, $Φ$, and other microstructural parameters is proposed and a study of the effect of inter-fiber spacing on $\mathcal{K}$, the permeability tensor, is performed. This task was achieved using parallel computation and over 460 simulations were carried out in two-dimensional RVEs consisting of over 555 fibers.
Keywords: Permeability; Fibrous Media; Finite Element Method; Level-set.