Abstract The viscous flow of two immiscible fluids in a
porous medium on the Darcy scale is governed by a system of nonlinear
parabolic equations. If infinite mobility of one phase can be assumed
(e.g., in soil layers in contact with the atmosphere) the system can be
substituted by the scalar Richards model. Thus, the porous medium domain
may be partitioned into disjoint subdomains where either the full
two-phase or the simplified Richards model dynamics are valid. Extending
the previously considered one-model situations we suggest coupling
conditions for this hybrid model approach. Based on an Euler implicit
discretization, a linear iterative (L-type) domain decomposition scheme
is proposed, and proved to be convergent. The theoretical findings are
verified by a comparative numerical study that in particular confirms
the efficiency of the hybrid ansatz as compared to full two-phase model
computations.
%0 Journal Article
%1 SeusRadurohde23
%A Seus, David
%A Radu, Florin A.
%A Rohde, Christian
%D 2023
%J Numer. Methods Partial Differential Equations
%K from:brittalenz am vorlaeufig IANS
%N 1
%P 622-656
%R https://doi.org/10.1002/num.22906
%T Towards hybrid two-phase modelling using linear domain
decomposition
%U https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22906
%V 39
%X Abstract The viscous flow of two immiscible fluids in a
porous medium on the Darcy scale is governed by a system of nonlinear
parabolic equations. If infinite mobility of one phase can be assumed
(e.g., in soil layers in contact with the atmosphere) the system can be
substituted by the scalar Richards model. Thus, the porous medium domain
may be partitioned into disjoint subdomains where either the full
two-phase or the simplified Richards model dynamics are valid. Extending
the previously considered one-model situations we suggest coupling
conditions for this hybrid model approach. Based on an Euler implicit
discretization, a linear iterative (L-type) domain decomposition scheme
is proposed, and proved to be convergent. The theoretical findings are
verified by a comparative numerical study that in particular confirms
the efficiency of the hybrid ansatz as compared to full two-phase model
computations.
@article{SeusRadurohde23,
abstract = {Abstract The viscous flow of two immiscible fluids in a
porous medium on the Darcy scale is governed by a system of nonlinear
parabolic equations. If infinite mobility of one phase can be assumed
(e.g., in soil layers in contact with the atmosphere) the system can be
substituted by the scalar Richards model. Thus, the porous medium domain
may be partitioned into disjoint subdomains where either the full
two-phase or the simplified Richards model dynamics are valid. Extending
the previously considered one-model situations we suggest coupling
conditions for this hybrid model approach. Based on an Euler implicit
discretization, a linear iterative (L-type) domain decomposition scheme
is proposed, and proved to be convergent. The theoretical findings are
verified by a comparative numerical study that in particular confirms
the efficiency of the hybrid ansatz as compared to full two-phase model
computations.},
added-at = {2022-11-07T09:23:36.000+0100},
author = {Seus, David and Radu, Florin A. and Rohde, Christian},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2135b531d0a43fa2e3cea1b2773367c75/mathematik},
doi = {https://doi.org/10.1002/num.22906},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.22906},
interhash = {7855afb8f3dec609892dccee7102c86d},
intrahash = {135b531d0a43fa2e3cea1b2773367c75},
journal = {Numer. Methods Partial Differential Equations},
keywords = {from:brittalenz am vorlaeufig IANS},
number = 1,
pages = {622-656},
timestamp = {2023-03-03T09:06:44.000+0100},
title = {Towards hybrid two-phase modelling using linear domain
decomposition},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22906},
volume = 39,
year = 2023
}