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On a front evolution in porous media with a source–analysis and numerics

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Abstract

We analyze evolution of the interface between immiscible fluids of different densities in porous media. The fluids can be compressible (CO 2 or natural gases) or incompressible (oil, water). We rigorously prove that, if the heavier fluid is on the top and there are no sink or source, a tip of the interface will move in the direction of the gravity (if the tip is directed toward the bottom) or the buoyancy (if the tip is directed toward the top).We also showhowthe sink/source influence propagation of the interface and provide numerical examples.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia

    Maroje Marohnić & Darko Mitrović

  2. Faculty of Mathematics, University of Montenegro, Cetinjski put bb, 81000, Podgorica, Montenegro

    Darko Mitrović

  3. Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000, Zagreb, Croatia

    Andrej Novak

Authors
  1. Maroje Marohnić
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  2. Darko Mitrović
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  3. Andrej Novak
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Correspondence to Andrej Novak.

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Marohnić, M., Mitrović, D. & Novak, A. On a front evolution in porous media with a source–analysis and numerics. Bull Braz Math Soc, New Series 47, 521–532 (2016). https://doi.org/10.1007/s00574-016-0166-6

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  • DOI: https://doi.org/10.1007/s00574-016-0166-6

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