We present the numerical implementation of a model that couples single-phase free and two-phase porous-media flow and transport with the focus on the treatment of the interface conditions. The model concept is based on the two-domain approach and on non-isothermal compositional submodels. These are coupled by interface conditions accounting for mass, momentum and energy transfer, and guaranteeing continuity of fluxes. A vertex-centred finite-volume scheme is used throughout the domain and a global matrix is solved for the whole system incorporating the coupling matrices. The fluxes at the interface are calculated indirectly via a flux balance from the adjacent finite-volume boxes. Numerical examples, representing evaporation from partially saturated porous media influenced by an ambient air flow, illustrate the evolution of saturation and temperature in a reference case and demonstrate the coupling concept. Furthermore, the effect of temperature, Beavers–Joseph coefficient and permeability on the evaporation process are examined with a series of simulations. In the presented set-ups, the choice of the Beavers–Joseph coefficient has a negligible influence on the evaporation rate across the interface.
%0 Journal Article
%1 10.1093/imamat/hxs048
%A Baber, Katherina
%A Mosthaf, Klaus
%A Flemisch, Bernd
%A Helmig, Rainer
%A Müthing, Steffen
%A Wohlmuth, Barbara
%D 2012
%J IMA Journal of Applied Mathematics
%K EXC310 curated
%N 6
%P 887-909
%R 10.1093/imamat/hxs048
%T Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow
%U https://doi.org/10.1093/imamat/hxs048
%V 77
%X We present the numerical implementation of a model that couples single-phase free and two-phase porous-media flow and transport with the focus on the treatment of the interface conditions. The model concept is based on the two-domain approach and on non-isothermal compositional submodels. These are coupled by interface conditions accounting for mass, momentum and energy transfer, and guaranteeing continuity of fluxes. A vertex-centred finite-volume scheme is used throughout the domain and a global matrix is solved for the whole system incorporating the coupling matrices. The fluxes at the interface are calculated indirectly via a flux balance from the adjacent finite-volume boxes. Numerical examples, representing evaporation from partially saturated porous media influenced by an ambient air flow, illustrate the evolution of saturation and temperature in a reference case and demonstrate the coupling concept. Furthermore, the effect of temperature, Beavers–Joseph coefficient and permeability on the evaporation process are examined with a series of simulations. In the presented set-ups, the choice of the Beavers–Joseph coefficient has a negligible influence on the evaporation rate across the interface.
@article{10.1093/imamat/hxs048,
abstract = {{We present the numerical implementation of a model that couples single-phase free and two-phase porous-media flow and transport with the focus on the treatment of the interface conditions. The model concept is based on the two-domain approach and on non-isothermal compositional submodels. These are coupled by interface conditions accounting for mass, momentum and energy transfer, and guaranteeing continuity of fluxes. A vertex-centred finite-volume scheme is used throughout the domain and a global matrix is solved for the whole system incorporating the coupling matrices. The fluxes at the interface are calculated indirectly via a flux balance from the adjacent finite-volume boxes. Numerical examples, representing evaporation from partially saturated porous media influenced by an ambient air flow, illustrate the evolution of saturation and temperature in a reference case and demonstrate the coupling concept. Furthermore, the effect of temperature, Beavers–Joseph coefficient and permeability on the evaporation process are examined with a series of simulations. In the presented set-ups, the choice of the Beavers–Joseph coefficient has a negligible influence on the evaporation rate across the interface.}},
added-at = {2024-01-11T14:11:39.000+0100},
author = {Baber, Katherina and Mosthaf, Klaus and Flemisch, Bernd and Helmig, Rainer and Müthing, Steffen and Wohlmuth, Barbara},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/28307ffa60db99388c35567b41a8d5a5a/simtech},
doi = {10.1093/imamat/hxs048},
eprint = {https://academic.oup.com/imamat/article-pdf/77/6/887/2366676/hxs048.pdf},
interhash = {e915e35b4d7439ac2d6c012a2c5978ac},
intrahash = {8307ffa60db99388c35567b41a8d5a5a},
issn = {0272-4960},
journal = {IMA Journal of Applied Mathematics},
keywords = {EXC310 curated},
number = 6,
pages = {887-909},
timestamp = {2024-02-26T18:00:29.000+0100},
title = {{Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow}},
url = {https://doi.org/10.1093/imamat/hxs048},
volume = 77,
year = 2012
}
