We study the interaction between a poroelastic medium and a fracture filled with fluid. The flow in the fracture is described by the Brinkman equations for an incompressible fluid and the poroelastic medium by the quasi-static Biot model. The two models are fully coupled via the kinematic and dynamic conditions. The Brinkman equations are then averaged over the cross-sections, giving rise to a reduced flow model on the fracture midline. We derive suitable interface and closure conditions between the Biot system and the dimensionally reduced Brinkman model that guarantee solvability of the resulting coupled problem. We design and analyze a numerical discretization scheme based on finite elements in space and the Backward Euler in time, and perform numerical experiments to compare the behavior of the reduced model to the full-dimensional formulation and study the response of the model with respect to its parameters.
Accepté le :
DOI : 10.1051/m2an/2016069
Mots clés : Reduced model, fracture flow, poroelasticity
@article{M2AN_2017__51_4_1429_0, author = {Buka\v{c}, Martina and Yotov, Ivan and Zunino, Paolo}, title = {Dimensional model reduction for flow through fractures in poroelastic media}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1429--1471}, publisher = {EDP-Sciences}, volume = {51}, number = {4}, year = {2017}, doi = {10.1051/m2an/2016069}, zbl = {1372.76100}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2016069/} }
TY - JOUR AU - Bukač, Martina AU - Yotov, Ivan AU - Zunino, Paolo TI - Dimensional model reduction for flow through fractures in poroelastic media JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1429 EP - 1471 VL - 51 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016069/ DO - 10.1051/m2an/2016069 LA - en ID - M2AN_2017__51_4_1429_0 ER -
%0 Journal Article %A Bukač, Martina %A Yotov, Ivan %A Zunino, Paolo %T Dimensional model reduction for flow through fractures in poroelastic media %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1429-1471 %V 51 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016069/ %R 10.1051/m2an/2016069 %G en %F M2AN_2017__51_4_1429_0
Bukač, Martina; Yotov, Ivan; Zunino, Paolo. Dimensional model reduction for flow through fractures in poroelastic media. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1429-1471. doi : 10.1051/m2an/2016069. http://www.numdam.org/articles/10.1051/m2an/2016069/
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