We introduce a Darcy‐scale model to describe compressible multicomponent flow in a fully saturated porous medium. In order to capture cross‐diffusive effects between the different species correctly, we make use of the Maxwell–Stefan theory in a thermodynamically consistent way.
For inviscid flow, the model turns out to be a nonlinear system of hyperbolic balance laws. We show that the dissipative structure of the Maxwell‐Stefan operator permits to guarantee the existence of global classical solutions for initial data close to equilibria. Furthermore, it is proven by relative entropy techniques that solutions of the Darcy‐scale model tend in a certain long‐time regime to solutions of a parabolic limit system.
%0 Journal Article
%1 ostrowski2019compressible
%A Ostrowski, Lukas
%A Rohde, Christian
%D 2020
%J Math. Meth. Appl. Sci.
%K ians imported vorlaeufig
%P 1-22
%T Compressible multi-component flow in porous media with Maxwell-Stefan diffusion
%U https://doi.org/10.1002/mma.6185
%X We introduce a Darcy‐scale model to describe compressible multicomponent flow in a fully saturated porous medium. In order to capture cross‐diffusive effects between the different species correctly, we make use of the Maxwell–Stefan theory in a thermodynamically consistent way.
For inviscid flow, the model turns out to be a nonlinear system of hyperbolic balance laws. We show that the dissipative structure of the Maxwell‐Stefan operator permits to guarantee the existence of global classical solutions for initial data close to equilibria. Furthermore, it is proven by relative entropy techniques that solutions of the Darcy‐scale model tend in a certain long‐time regime to solutions of a parabolic limit system.
@article{ostrowski2019compressible,
abstract = {We introduce a Darcy‐scale model to describe compressible multicomponent flow in a fully saturated porous medium. In order to capture cross‐diffusive effects between the different species correctly, we make use of the Maxwell–Stefan theory in a thermodynamically consistent way.
For inviscid flow, the model turns out to be a nonlinear system of hyperbolic balance laws. We show that the dissipative structure of the Maxwell‐Stefan operator permits to guarantee the existence of global classical solutions for initial data close to equilibria. Furthermore, it is proven by relative entropy techniques that solutions of the Darcy‐scale model tend in a certain long‐time regime to solutions of a parabolic limit system.},
added-at = {2020-01-21T08:43:20.000+0100},
author = {Ostrowski, Lukas and Rohde, Christian},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2e8715d6c8d3eeece8eaaf74f68aa40a7/mathematik},
interhash = {1196903fb4af972e8057d239bf8afd04},
intrahash = {e8715d6c8d3eeece8eaaf74f68aa40a7},
journal = {Math. Meth. Appl. Sci. },
keywords = {ians imported vorlaeufig},
pages = {1-22},
timestamp = {2020-03-27T19:14:46.000+0100},
title = {Compressible multi-component flow in porous media with Maxwell-Stefan diffusion},
url = {https://doi.org/10.1002/mma.6185},
year = 2020
}
