Metzger S, Knabner P (2021)
Publication Type: Journal article
Publication year: 2021
Book Volume: 19
Pages Range: 320-343
Issue: 1
DOI: 10.1137/19M1287705
It is well known that the generalized Darcy law describing multiphase flow in porous media has some shortcomings. In particular, it cannot explain hysteresis effects in the capillary pressure--saturation curve which have been observed in measurements. In this work, we derive a numerically tractable micro-macro model including coupled generalized Darcy's laws that still includes the microscale dynamics which are responsible, e.g., for hysteresis effects. For this purpose, we extend the two-scale expansion approach of periodic homogenization to include different time scales which allows us to start from a fully instationary Navier--Stokes--Cahn--Hilliard model at the pore scale as microscale. Identifying and separating the time scales allows us to derive local fast scale equations describing the microscale dynamics and global slow-scale equations giving rise to the macroscopic Darcy law.
APA:
Metzger, S., & Knabner, P. (2021). Homogenization of Two-Phase Flow in Porous Media From Pore to Darcy Scale: A Phase-Field Approach. Multiscale Modeling & Simulation, 19, 320-343. https://doi.org/10.1137/19M1287705
MLA:
Metzger, Stefan, and Peter Knabner. "Homogenization of Two-Phase Flow in Porous Media From Pore to Darcy Scale: A Phase-Field Approach." Multiscale Modeling & Simulation 19 (2021): 320-343.
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