14-17 May 2018
New Orleans
US/Central timezone

A new coupled approach for numerically solving convection-diffusion problems with discontinuous capillary pressure

16 May 2018, 17:04
New Orleans

New Orleans

Poster + 3 Minute Pitch MS 2.08: Recent Advances in Multiscale Methods and Uncertainty Quantification Parallel 8-H


Dr Arthur Santo (University of Campinas)


In this work, we show an alternative way of handling the spatially discontinuous capillary pressure models in two-phase flow in porous media. This topic is very challenging and has also been studied theoretically and numerically in recent works [1,2,3]. We propose a new numerical formulation, by combining mixed hybrid finite element and finite volume discretization strategies along with novel coupling conditions at interfaces for numerically solving convection-diffusion problems with gravity and diffusive discontinuous capillary pressure. The novelties are twofold: 1) a reinterpretation of the Robin interface conditions between elements to accommodate the nontrivial effects of heterogeneities in capillary pressure and 2) the use of a conservative finite volume framework for approximation of the first-order hyperbolic flux in a robust fashion as a source term in the fully coupled formulation to preserve the delicate nonlinear balance with the diffusive operator. By following [4], we also present preliminary results and further directions that relates the new approach to multiscale formulations for porous media transport problems in the presence of high contrast geological properties.


[1] B. Andreianov, Clément Cancès, Vanishing capillarity solutions of Buckley-Leverett equation with gravity in two-rocks’ medium, Computational Geosciences 17(3) (2013) 551–572.

[2] E. Abreu, Numerical modelling of three-phase immiscible flow in heterogeneous porous media with gravitational effects, Mathematics and Computers in Simulation 97 (2014) 234-259.

[3] P. Bastian, A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure, Computational Geosciences 18(5) (2014) 779-796.

[4] Arthur Santo, Conservative numerical formulations for approximating hyperbolic models with source terms and related transport models. University of Campinas, Institute of Mathematics, Statistics and Scientific Computing (2017).

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Primary authors

Dr Arthur Santo (University of Campinas) Prof. Eduardo Abreu (University of Campinas, Sao Paulo, Brazil)

Presentation Materials