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Analysis of a linearization scheme for an interior penalty discontinuous Galerkin method for two‐phase flow in porous media with dynamic capillarity effects
Author(s) -
Karpinski Stefan,
Pop Iuliu Sorin,
Radu Florin Adrian
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5526
Subject(s) - linearization , mathematics , compressibility , galerkin method , porous medium , computation , regularization (linguistics) , mathematical analysis , flow (mathematics) , incompressible flow , nonlinear system , porosity , mechanics , computer science , geometry , algorithm , physics , engineering , geotechnical engineering , quantum mechanics , artificial intelligence
Summary We present a linearization scheme for an interior penalty discontinuous Galerkin method for two‐phase porous media flow model, which includes dynamic effects on the capillary pressure. The fluids are assumed immiscible and incompressible, and the solid matrix non‐deformable. The physical laws are approximated in their original form, without using the global or complementary pressures. The linearization scheme does not require any regularization step. Furthermore, in contrast with Newton or Picard methods, there is no computation of derivatives involved. We prove rigourously that the scheme is robust and linearly convergent. We make an extensive parameter study to compare the behaviour of the L‐scheme with the Newton method. Copyright © 2017 John Wiley & Sons, Ltd.