Nonlinear Preconditioning Strategies for Two-Phase Flows in Porous Media Discretized by a Fully Implicit Discontinuous Galerkin Method

A Hybridized Crouziex-Raviart Nonconforming Finite Element and Discontinuous Galerkin Method for a Two-Phase Flow in the Porous Media

In this study, we present a numerical solution for the two-phase incompressible flow in the porous media under isothermal condition using a hybrid of the linear lower-order nonconforming finite element and the interior penalty discontinuous Galerkin (DG) method. This hybridization is developed for the first time in the two-phase modeling and considered as the main novelty of this research.The p...

A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure

In this paper we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG formulation with weighted averages and is based on a wetting-phase potential / capillary potential formulation of the twophase flow system. After discretizing ...

A hybridizable discontinuous Galerkin method for two-phase flow in heterogeneous porous media

We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equations. The equations are discretized using a hybridizable discontinuous Galerkin (HDG) method. The proposed method is of high order, conserves global/local mass balance, and the number of globally coupled degrees of fre...

Discontinuous Galerkin finite element method for shallow two-phase flows

We present a discontinuous Galerkin finite element method for two depth-averaged two-phase flow models. One of these models contains nonconservative products for which we developed a discontinuous Galerkin finite element formulation in Rhebergen et al. (2008) J. Comput. Phys. 227, 1887-1922. The other model is a new depth-averaged two-phase flow model we introduce for shallow two-phase flows th...

Optimized Schwarz method for solving time-harmonic Maxwell's equations discretized by a discontinuous Galerkin method