A data-driven model order reduction approach for Stokes flow through random porous media
This work addresses the problem of high computational costs in fluid dynamics simulations for researchers and engineers in porous media, though it is incremental as it builds on existing Darcy-type approximations.
The authors tackled the computational expense of simulating Stokes flow through random porous media by proposing a data-driven reduced-order model that learns a map from fine-scale topology to effective diffusivity using only tens of full-order runs, significantly accelerating uncertainty quantification tasks.
Direct numerical simulation of Stokes flow through an impermeable, rigid body matrix by finite elements requires meshes fine enough to resolve the pore-size scale and is thus a computationally expensive task. The cost is significantly amplified when randomness in the pore microstructure is present and therefore multiple simulations need to be carried out. It is well known that in the limit of scale-separation, Stokes flow can be accurately approximated by Darcy's law with an effective diffusivity field depending on viscosity and the pore-matrix topology. We propose a fully probabilistic, Darcy-type, reduced-order model which, based on only a few tens of full-order Stokes model runs, is capable of learning a map from the fine-scale topology to the effective diffusivity and is maximally predictive of the fine-scale response. The reduced-order model learned can significantly accelerate uncertainty quantification tasks as well as provide quantitative confidence metrics of the predictive estimates produced.