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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 757–776 (Mi semr1093)  

Computational mathematics

On the streamline upwind scheme of solution to the filtration problem

M. I. Ivanova, I. A. Kremerab, Yu. M. Laevskyab

a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6, Akad. Lavrent'eva ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia

Abstract: The work is devoted to one of the approaches in the numerical simulation of filtration processes of a two-phase incompressible fluid. Bukley – Leverett problem is considered with solutions of a shock wave type. Within the mixed finite element method upwind algorithm for solution to equation for saturation is proposed, which gives solutions without numerical oscillations at the discontinuity. Special attention is paid to a new approach to solving the degenerate Neumann problem in a mixed formulation for the pressure and total flow velocity. The work is accompanied by an illustration of the results of numerical experiments for 3D problem.

Keywords: immiscible fluid flow, filtration, two-phase fluid, injection well, production well, mixed finite element method, upwind scheme.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0315-2016-0008
Russian Science Foundation 19-11-00048
Russian Foundation for Basic Research 16-29-15122_офи_м


DOI: https://doi.org/10.33048/semi.2019.16.051

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Bibliographic databases:

UDC: 519.63
MSC: 65M06
Received March 18, 2019, published June 7, 2019

Citation: M. I. Ivanov, I. A. Kremer, Yu. M. Laevsky, “On the streamline upwind scheme of solution to the filtration problem”, Sib. Èlektron. Mat. Izv., 16 (2019), 757–776

Citation in format AMSBIB
\Bibitem{IvaKreLae19}
\by M.~I.~Ivanov, I.~A.~Kremer, Yu.~M.~Laevsky
\paper On the streamline upwind scheme of solution to the filtration problem
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 757--776
\mathnet{http://mi.mathnet.ru/semr1093}
\crossref{https://doi.org/10.33048/semi.2019.16.051}


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