Total-velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure - Archive ouverte HAL Access content directly
Journal Articles IMA Journal of Numerical Analysis Year : 2021

Total-velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure

Konstantin Brenner
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Jerome Droniou
Roland Masson

Abstract

This work proposes a finite volume scheme for two-phase Darcy flow in heterogeneous porous media with different rock types. The fully implicit discretization is based on cell centered as well as face centered degrees of freedom in order to capture accurately the nonlinear transmission conditions at different rock type interfaces. These conditions play a major role in the flow dynamics. The scheme is formulated with natural physical unknowns avoiding the cumbersome use of the global pressure. It combines a Two-Point Flux Approximation of the gradient normal fluxes with a Hybrid Upwinding approximation of the transport terms. The convergence of the scheme to a weak solution is established taking into account discontinuous capillary pressure at different rock type interfaces and the degeneracy of the phase mobilities. Numerical experiments show the additional robustness of the proposed discretization compared with the classical Phase Potential Upwinding approach.
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Dates and versions

hal-02957054 , version 1 (04-10-2020)
hal-02957054 , version 2 (25-02-2021)

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Konstantin Brenner, Jerome Droniou, Roland Masson, El Houssaine H Quenjel. Total-velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure. IMA Journal of Numerical Analysis, 2021, ⟨10.1093/imanum/drab018⟩. ⟨hal-02957054v2⟩
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