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. Coupled, hybrid-dimensional models can be much more efficient by simplifying the porous domain, e.g., in terms of a pore-network model. In this work, we present a coupled pore-network/free-flow model taking into account pore-scale slip at the local interfaces between free flow and the pores. We consider two-dimensional and three-dimensional setups and show that our proposed slip condition can significantly increase the coupled model's accuracy: compared to fully resolved equidimensional numerical reference solutions, the normalized errors for velocity are reduced by a factor of more than five, depending on the flow configuration. A pore-scale slip parameter \$\$\backslashbeta \_\\\\\backslashrm pore\\\\\$\$$\beta$porerequired by the slip condition was determined numerically in a preprocessing step. We found a linear scaling behavior of \$\$\backslashbeta \_\\\\\backslashrm pore\\\\\$\$$\beta$porewith the size of the interface pore body for three-dimensional and two-dimensional domains. The slip condition can thus be applied without incurring any run-time cost. In the last section of this work, we used the coupled model to recalculate a microfluidic experiment where we additionally exploited the flat structure of the micromodel which permits the use of a quasi-3D free-flow model. The extended coupled model is accurate and efficient.
%0 Journal Article
%1 Weishaupt2020
%A Weishaupt, K.
%A Terzis, A.
%A Zarikos, I.
%A Yang, G.
%A Flemisch, B.
%A de Winter, D. A. M.
%A Helmig, R.
%D 2020
%J Transport in Porous Media
%K pa-a rp-a2 sfb1313
%R 10.1007/s11242-020-01477-y
%T A Hybrid-Dimensional Coupled Pore-Network/Free-Flow Model Including Pore-Scale Slip and Its Application to a Micromodel Experiment
%U https://doi.org/10.1007/s11242-020-01477-y
%X Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier--Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Coupled, hybrid-dimensional models can be much more efficient by simplifying the porous domain, e.g., in terms of a pore-network model. In this work, we present a coupled pore-network/free-flow model taking into account pore-scale slip at the local interfaces between free flow and the pores. We consider two-dimensional and three-dimensional setups and show that our proposed slip condition can significantly increase the coupled model's accuracy: compared to fully resolved equidimensional numerical reference solutions, the normalized errors for velocity are reduced by a factor of more than five, depending on the flow configuration. A pore-scale slip parameter \$\$\backslashbeta \_\\\\\backslashrm pore\\\\\$\$$\beta$porerequired by the slip condition was determined numerically in a preprocessing step. We found a linear scaling behavior of \$\$\backslashbeta \_\\\\\backslashrm pore\\\\\$\$$\beta$porewith the size of the interface pore body for three-dimensional and two-dimensional domains. The slip condition can thus be applied without incurring any run-time cost. In the last section of this work, we used the coupled model to recalculate a microfluidic experiment where we additionally exploited the flat structure of the micromodel which permits the use of a quasi-3D free-flow model. The extended coupled model is accurate and efficient.
@article{Weishaupt2020,
abstract = {Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier--Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Coupled, hybrid-dimensional models can be much more efficient by simplifying the porous domain, e.g., in terms of a pore-network model. In this work, we present a coupled pore-network/free-flow model taking into account pore-scale slip at the local interfaces between free flow and the pores. We consider two-dimensional and three-dimensional setups and show that our proposed slip condition can significantly increase the coupled model's accuracy: compared to fully resolved equidimensional numerical reference solutions, the normalized errors for velocity are reduced by a factor of more than five, depending on the flow configuration. A pore-scale slip parameter {\$}{\$}{\backslash}beta {\_}{\{}{\{}{\{}{\{}{\backslash}rm pore{\}}{\}}{\}}{\}}{\$}{\$}$\beta$porerequired by the slip condition was determined numerically in a preprocessing step. We found a linear scaling behavior of {\$}{\$}{\backslash}beta {\_}{\{}{\{}{\{}{\{}{\backslash}rm pore{\}}{\}}{\}}{\}}{\$}{\$}$\beta$porewith the size of the interface pore body for three-dimensional and two-dimensional domains. The slip condition can thus be applied without incurring any run-time cost. In the last section of this work, we used the coupled model to recalculate a microfluidic experiment where we additionally exploited the flat structure of the micromodel which permits the use of a quasi-3D free-flow model. The extended coupled model is accurate and efficient.},
added-at = {2020-09-16T11:27:18.000+0200},
author = {Weishaupt, K. and Terzis, A. and Zarikos, I. and Yang, G. and Flemisch, B. and de Winter, D. A. M. and Helmig, R.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21e975c12a224e895ff79ec0ac41e76ff/sfb1313-puma},
day = 14,
doi = {10.1007/s11242-020-01477-y},
interhash = {3b2ae353b99b661d7778905409e8b76d},
intrahash = {1e975c12a224e895ff79ec0ac41e76ff},
issn = {1573-1634},
journal = {Transport in Porous Media},
keywords = {pa-a rp-a2 sfb1313},
month = sep,
timestamp = {2020-09-16T09:27:18.000+0200},
title = {A Hybrid-Dimensional Coupled Pore-Network/Free-Flow Model Including Pore-Scale Slip and Its Application to a Micromodel Experiment},
url = {https://doi.org/10.1007/s11242-020-01477-y},
year = 2020
}
