A staggered finite element procedure for the coupled Stokes-Biot system with fluid entry resistance

• Published in: Computational geosciences Vol. 24; no. 4; pp. 1497 - 1522
• Main Authors: Bergkamp, E. A., Verhoosel, C. V., Remmers, J. J. C., Smeulders, D. M. J.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-08-2020; Springer Nature B.V
• Subjects: Computational fluid dynamics; Computer simulation; Earth and Environmental Science; Earth Sciences; Formability; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Interface phenomena; Mathematical Modeling and Industrial Mathematics; Mathematical models; Membrane permeability; Modelling; Original Paper; Parameter sensitivity; Permeability; Porous media; Pressure; Pressure gradients; Pressure jump; Procedures; Simulation; Skin; Skin effect; Slip; Slip resistance; Soil Science & Conservation; Viscous flow; Beavers-Joseph-Saffman condition; Staggered solution procedure; Fluid entry resistance; Finite element simulation; Interface coupling; Deformable porous media; Skin effect; Stokes-Biot model
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-019-09931-7

We develop a staggered finite element procedure for the coupling of a free viscous flow with a deformable porous medium, in which interface phenomena related to the skin effect can be incorporated. The basis of the developed simulation procedure is the coupled Stokes-Biot model, which is supplemented with interface conditions to mimic interface-related phenomena. Specifically, the fluid entry resistance parameter is used to relate the fluid flux through the interface to the pressure jump across the interface. The attainable jump in pressure over the interface provides an effective way of modeling sharp pressure gradients associated with the possibly reduced permeability of the interface on account of pore clogging. In addition to the fluid entry resistance parameter, the developed simulation strategy also includes the possibility of modeling fluid slip over the porous medium. Sensitivity studies are presented for both the fluid entry resistance parameter and the slip coefficient, and representative two- and three-dimensional test cases are presented to demonstrate the applicability of the developed simulation technique.