Model reduction for coupled free flow over porous media: a hybrid dimensional pore network model approach

Abstract

Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier-Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Model reduction allows to decrease a model's complexity while maintaining an acceptable degree of accuracy. Starting from a fully resolved three-dimensional numerical model, which is compared to high-resolution micro-PIV experimental data obtained from a previous study (Terzis et al.,2019), we perform a two-fold model reduction: first, a quasi-3D model incorporating a wall friction term is successfully compared to the fully resolved model. Second, we employ a pore-network model to account for the porous part of the domain and couple it to the quasi-3D model which still resolves the free-flow part of the domain (Weishaupt et al., 2019). We have extended this coupling approach here to include slip velocities at the pore throats intersecting with the free-flow domain. The proposed method is simple, accurate and comes at no additional run-time penalty. The coupled model deviates by less than 10 % from the other two model concepts. Several hours of run-time was required for the three-dimensional model compared to eleven and five minutes necessary for the quasi-3D and coupled model which highlights the benefits of model reduction.