Mathematical analysis of variable density flows in porous media
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We consider a simple model describing the motion of a two-component mixture through a porous medium. We discuss well posedness of the associated initial-boundary value problem, in particular, with respect to the choice of boundary and far-field conditions. The existence of global-in-time solutions is proved in the ideal case when the fluid occupies the whole physical space. Finally, similar results are obtained also for the boundary value problems in the simplified 1-D geometry.
KeywordsVariable density flow Flows in porous media Global-in-time solutions
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- 1.Ph. Clément, C. J. van Duijn, and Shuanhu Li. On a nonlinear elliptic-parabolic partial differential equation system in a two-dimensional groundwater flow problem. SIAM J. Math. Anal., 23(4):836–851, 1992.Google Scholar
- 4.van C.J. Duijn, L.A. Peletier, and R.-J. Schotting. Brine transport in porous media: self-similar solutions. Adv. Water Resources, 22:285–297, 1998.Google Scholar
- 6.D. Hilhorst, Huy Cuong Vu Do, and Y. Wang. A finite volume method for density driven flows in porous media. In CEMRACS’11: Multiscale coupling of complex models in scientific computing, volume 38 of ESAIM Proc., pages 376–386. EDP Sci., Les Ulis, 2012.Google Scholar
- 7.B. Johannsen. Numerische Aspekte dichtegetriebener Strömung in porösen Medien. Habilitation Thesis - https://sites.google.com/site/klausjohannsen/publications, 2004.
- 8.O. Kolditz, R. Ratke, H.-J.G. Diersch, and W. Zielke. Coupled groundwater flow and transport: 1. Verification of variable density flow and transport model. Adv. Water Resources, 21:27–46, 1998.Google Scholar