We study single-phase flow in a fractured porous medium at
a macroscopic scale that allows to model fractures individually. The
flow is governed by Darcy's law in both fractures and porous matrix. We
derive a new mixed-dimensional model, where fractures are represented by
$(n-1)$-dimensional interfaces between $n$-dimensional subdomains for
$n2$. In particular, we suggest a generalization of the model
in~[22] by accounting for asymmetric fractures with spatially varying
aperture. Thus, the new model is particularly convenient for the
description of surface roughness or for modeling curvilinear or winding
fractures. The wellposedness of the new model is proven under
appropriate conditions. Further, we formulate a discontinuous Galerkin
discretization of the new model and validate the model by performing
two- and three-dimensional numerical experiments.
%0 Journal Article
%1 burbulla2022flow
%A Burbulla, Samuel
%A Hörl, Maximilian
%A Rohde, Christian
%D 2023
%J SIAM J. Sci. Comput
%K test5
%N 4
%P A1519-A1544
%R 10.1137/22M1510406
%T Flow in Porous Media with Fractures of Varying Aperture
%U https://doi.org/10.1137/22M1510406
%V 45
%X We study single-phase flow in a fractured porous medium at
a macroscopic scale that allows to model fractures individually. The
flow is governed by Darcy's law in both fractures and porous matrix. We
derive a new mixed-dimensional model, where fractures are represented by
$(n-1)$-dimensional interfaces between $n$-dimensional subdomains for
$n2$. In particular, we suggest a generalization of the model
in~[22] by accounting for asymmetric fractures with spatially varying
aperture. Thus, the new model is particularly convenient for the
description of surface roughness or for modeling curvilinear or winding
fractures. The wellposedness of the new model is proven under
appropriate conditions. Further, we formulate a discontinuous Galerkin
discretization of the new model and validate the model by performing
two- and three-dimensional numerical experiments.
@article{burbulla2022flow,
abstract = {We study single-phase flow in a fractured porous medium at
a macroscopic scale that allows to model fractures individually. The
flow is governed by Darcy's law in both fractures and porous matrix. We
derive a new mixed-dimensional model, where fractures are represented by
$(n-1)$-dimensional interfaces between $n$-dimensional subdomains for
$n\ge 2$. In particular, we suggest a generalization of the model
in~[22] by accounting for asymmetric fractures with spatially varying
aperture. Thus, the new model is particularly convenient for the
description of surface roughness or for modeling curvilinear or winding
fractures. The wellposedness of the new model is proven under
appropriate conditions. Further, we formulate a discontinuous Galerkin
discretization of the new model and validate the model by performing
two- and three-dimensional numerical experiments.},
added-at = {2024-04-15T12:58:10.000+0200},
author = {Burbulla, Samuel and Hörl, Maximilian and Rohde, Christian},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2608038df73e2886cbe5c6681c09be78b/institutstest},
doi = {10.1137/22M1510406},
eprint = {https://doi.org/10.1137/22M1510406},
interhash = {966225b3cd5b5d0838e76b342356e493},
intrahash = {608038df73e2886cbe5c6681c09be78b},
journal = {SIAM J. Sci. Comput},
keywords = {test5},
number = 4,
pages = {A1519-A1544},
timestamp = {2024-05-14T13:51:39.000+0200},
title = {Flow in Porous Media with Fractures of Varying Aperture},
url = {https://doi.org/10.1137/22M1510406},
volume = 45,
year = 2023
}