Numerical Study for Two-Phase Flow with Gravity in Homogeneous and Piecewise-Homogeneous Porous Media
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In this work we study two-phase flow with gravity either in 1-rock homogeneous media or 2-rocks composed media, this phenomenon can be modeled by a non-linear scalar conservation law with continuous flux function or discontinuous flux function, respectively. Our study is essentially from a numerical point of view, we apply the new Lagrangian-Eulerian finite difference method developed by Abreu and Pérez and the Lax-Friedrichs classic method to obtain numerical entropic solutions. Comparisons between numerical and analytical solutions show the efficiency of the methods even for discontinuous flux function.
2012 ◽
Vol 64
(4)
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pp. 1025-1056
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2009 ◽
Vol 2009
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pp. 1-33
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2020 ◽
Vol 144
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pp. 107532
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2011 ◽
Vol 54
(9)
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pp. 2412-2420
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2020 ◽
Vol 191
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pp. 107173
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2020 ◽
Vol 140
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pp. 137-150
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