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 Proceedings of ISP RAS, 2018, Volume 30, Issue 5, Pages 197–212 (Mi tisp369)

Rock flow simulation by high-order quasi-characteristics scheme

M. P. Levin

Ivannikov Institute for System Programming of RAS

Abstract: A pure second-order scheme of quasi-characteristics based on a pyramidal stencil is applied to the numerical modelling of non-stationary two-phase flows through porous media with the essentially heterogeneous properties. In contrast to well-known other high-resolution schemes with monotone properties, this scheme preserves a second-order approximation in regions, where discontinuities of solutions arise, as well as monotone properties of numerical solutions in those regions despite of well-known Godunov theorem. It is possible because the scheme under consideration is defined on a non-fixed stencil and is a combination of two high-order approximation scheme solutions with different dispersion properties. A special criterion according to which, one or another admissible solution is chosen, plays a key role in this scheme. A simple criterion with local character suitable for parallel computations is proposed. Some numerical results showing the efficiency of present approach in computations of two-phase flows through porous media with strongly discontinuous penetration coefficients are presented.

Keywords: Quasi-Characteristics, Two-phase Porous Media Flows, Heterogeneous Media.

DOI: https://doi.org/10.15514/ISPRAS-2018-30(5)-12

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Citation: M. P. Levin, “Rock flow simulation by high-order quasi-characteristics scheme”, Proceedings of ISP RAS, 30:5 (2018), 197–212

Citation in format AMSBIB
\Bibitem{Lev18} \by M.~P.~Levin \paper Rock flow simulation by high-order quasi-characteristics scheme \jour Proceedings of ISP RAS \yr 2018 \vol 30 \issue 5 \pages 197--212 \mathnet{http://mi.mathnet.ru/tisp369} \crossref{https://doi.org/10.15514/ISPRAS-2018-30(5)-12} \elib{https://elibrary.ru/item.asp?id=36591035}