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Monotone nonlinear finite‐volume method for nonisothermal two‐phase two‐component flow in porous media
Author(s) -
Schneider Martin,
Flemisch Bernd,
Helmig Rainer
Publication year - 2016
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4352
Subject(s) - finite volume method , mathematics , nonlinear system , porous medium , monotone polygon , mathematical analysis , interpolation (computer graphics) , flow (mathematics) , finite element method , geometry , porosity , mechanics , physics , materials science , classical mechanics , thermodynamics , motion (physics) , quantum mechanics , composite material
Summary This article presents a new nonlinear finite‐volume scheme for the nonisothermal two‐phase two‐component flow equations in porous media. The face fluxes are approximated by a nonlinear two‐point flux approximation, where transmissibilities nonlinearly depend on primary variables. Thereby, we mainly follow the ideas proposed by Le Potier combined with a harmonic averaging point interpolation strategy for the approximation of arbitrary heterogeneous permeability fields on polygonal grids. The behavior of this interpolation strategy is analyzed, and its limitation for highly anisotropic permeability tensors is demonstrated. Moreover, the condition numbers of occurring matrices are compared with linear finite‐volume schemes. Additionally, the convergence behavior of iterative solvers is investigated. Finally, it is shown that the nonlinear scheme is more efficient than its linear counterpart. Copyright © 2016 John Wiley & Sons, Ltd.