This article is cited in 6 papers

Computational mathematics

On the streamline upwind scheme of solution to the filtration problem

M. I. Ivanov^a, I. A. Kremer^ab, Yu. M. Laevsky<sup>ab

a</sup> 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.

UDC: 519.63

MSC: 65M06

Received March 18, 2019, published June 7, 2019

DOI: 10.33048/semi.2019.16.051

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