An efficient discontinuous Galerkin method for two-phase flow modeling by conservative velocity projection

Abstract

Purpose – The purpose of this paper is to present a novel sequential implicit discontinuous Galerkin (DG) method for two-phase incompressible flow in porous media. It is based on the wetting phase pressure-saturation formulation with Robin boundary condition (Klieber and Riviere, 2006) using H(div) velocity projection. Design/methodology/approach – The local mass conservation and continuity of normal component of velocity across elements interfaces are enforced by a simple H(div) velocity projection in lowest order Raviart-Thomas (RT0) space. As further improvements, the authors use the weighted averages and the scaled penalties in spatial DG discretization. Moreover, the Chavent-Jaffre slope limiter, as a consistent non-oscillatory limiter, is used for saturation values to avoid the spurious oscillations. Findings – The proposed model is verified by a pseudo 1D Buckley-Leverett problem in homogeneous media. Two homogeneous and heterogeneous quarter five-spot benchmark problems and a random permeable medium are used to show the accuracy of the method at capturing the sharp front and illustrate the impact of proposed improvements. Research limitations/implications – The work illustrates incompressible two-phase flow behavior and the capillary pressure heterogeneity between different geological layers is assumed to be negligible. Practical implications – The proposed model can efficiently be used for modeling of two-phase flow in secondary recovery of petroleum reservoirs and tracing the immiscible contamination in porous media. Originality/value – The authors present an efficient sequential DG method for immiscible incompressible two-phase flow in porous media with improved performance for detection of sharp frontal interfaces and discontinuities.

Parallel discontinuous Galerkin finite element method for computing hyperbolic conservation law on unstructured meshes

“…An adaptive fully DG level set method was proposed for incompressible multiphase flows (Karakus et al , 2018). DGM for two-phrase flows were investigated by Jamei and Ghafouri (2016a, 2016b).…”

“…Moreover, discontinuous Galerkin methods require much more storage resources on unstructured grids. To improve the efficiency, the various numerical schemes and parallel algorithms are developed in literature (Luo et al , 2011; Xia et al , 2014; Zhang et al , 2019). Xia et al (2014) propose a parallel h-adaptive reconstructed DGM for three-dimensional compressible flows.…”