A sequential discontinuous Galerkin method for two-phase flow in deformable porous media. (English) Zbl 1507.76122
Summary: We formulate a numerical method for solving the two-phase flow poroelasticity equations. The scheme employs the interior penalty discontinuous Galerkin method and a sequential time-stepping method. The unknowns are the phase pressures and the displacement. Existence of the solution is proved. Three-dimensional numerical results show the accuracy and robustness of the proposed method.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76S05 | Flows in porous media; filtration; seepage |
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
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