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Numerical model reduction is exploited for computational homogenization of the model problem of a poroelastic medium under transient conditions. It is assumed that the displacement and pore pressure fields possess macro-scale and sub-scale (fluctuation) parts. A linearly independent reduced basis is constructed for the sub-scale pressure field using POD. The corresponding reduced basis for the displacement field is constructed in the spirit of the NTFA strategy. Evolution equations that define an apparent poro-viscoelastic macro-scale model are obtained from the continuity equation pertinent to the RVE. The present model represents an extension of models available in literature in the sense that the pressure gradient is allowed to have a non-zero macro-scale component in the nested    $$\hbox {FE}^2$$    FE  2setting. The numerical results show excellent agreement between the results from numerical model reduction and direct numerical simulation. It was also shown that even 3D RVEs give tractable solution times for full-fledged    $$\hbox {FE}^2$$    FE  2computations.

A poro-viscoelastic substitute model of fine-scale poroelasticity obtained from homogenization and numerical model reduction