A finite-element scheme is presented to investigate the permeability of fibrous porous medium in a bi-periodic domain such that a single cell problem with a small number of fiber filaments may represent a large number of repeated structures. Based on the fictitious domain method and the rigid-ring description, we use a fixed regular mesh for the entire domain, including the interior of fibers, and the fiber is described by its boundary only. A formal bi-periodicity has been implemented with the mortar-element method and fibers split by the domain boundary have been treated in a relatively easy way. To demonstrate the feasibility, examples of the regular fiber packing, the random fiber distribution and the fiber bundle problems have been investigated using the bi-periodic domain and compared with the literature.
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