SIAM Journal on Numerical Analysis
Discontinuous galerkin finite element methods applied to two-phase, air-water flow problems
Discontinuous galerkin finite element methods applied to two-phase, air-water flow problems
Understanding And Implementing the Finite Element Method
Understanding And Implementing the Finite Element Method
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Fully implicit discontinuous finite element methods for two-phase flow
Applied Numerical Mathematics
Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection
SIAM Journal on Numerical Analysis
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Hi-index | 7.29 |
We present a new version of the sequential discontinuous Galerkin method introduced in Ern et al. (2010) [32] for two-phase immiscible incompressible flows in heterogeneous porous media with a discontinuous capillary field. Here, a new implementation of the extended interface condition, that does not use the threshold saturation value at the interface and permits treatment of different residual saturations in different rocks, is considered. Another novel ingredient is the implicit treatment of the diffusion term and the non-linear interface conditions in the saturation equation. The proposed method is validated in two-dimensional test cases and confirms theoretically known optimal orders of convergence. The numerical experiments demonstrate that for two-dimensional interface problems the method exhibits better performance on moderately refined meshes, which is particularly important for multidimensional heterogeneous problems related to realistic field studies. We consider also two heterogeneous five-spot benchmark problems to assess the potential of the proposed method in simulations of reservoirs with discontinuous permeability and capillary pressure fields in different types of rock.