Abstract
One-dimensional problems of two-phase filtration of liquids (water and oil) in porous media are described by the Buckley–Leverett equations, the Darcy law, and the law of conservation of energy under certain initial and boundary conditions. In this paper, we propose an asymptotic method of constructing a solution of the problem and methods for resolution of singularities associated with shock waves that arise in the process. The method proposed is implemented numerically by using the Maple software.
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References
V. I. Arnold, Ordinary Differential Equations, MIT Press, Boston (1973).
A. V. Akhmetzyanov, A. G. Kushner, and V. V. Lychagin, “Mass and heat transport in the two-phase Buckley-Leverett model,” J. Geom. Phys., 113, 2–9 (2017).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 148, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory” (Ryazan, September 15–18, 2016), 2018.
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Boronin, I.A., Shevlyakov, A.A. Solution of Equations of a One-Dimensional Problem on Two-Phase Filtration in a Porous Medium with Account of Thermodynamical Effects by Using Geometric Methods. J Math Sci 248, 385–391 (2020). https://doi.org/10.1007/s10958-020-04878-y
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DOI: https://doi.org/10.1007/s10958-020-04878-y