Numerical simulation of water resources problems: Models, methods, and trends
Mechanistic modeling of water resources systems is a broad field with abundant challenges.
We consider classes of model formulations that are considered routine, the focus of current …
We consider classes of model formulations that are considered routine, the focus of current …
A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
P Bastian - Computational Geosciences, 2014 - Springer
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 …
method for incompressible two-phase flow with discontinuous capillary pressure. The spatial …
Fully mass-conservative IMPES schemes for incompressible two-phase flow in porous media
In this paper we consider fully mass-conservative numerical schemes for the simulation of
incompressible and immiscible two-phase flow in porous media with capillary pressure …
incompressible and immiscible two-phase flow in porous media with capillary pressure …
Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
C Cancès, C Guichard - Foundations of Computational Mathematics, 2017 - Springer
We present a numerical method for approximating the solutions of degenerate parabolic
equations with a formal gradient flow structure. The numerical method we propose …
equations with a formal gradient flow structure. The numerical method we propose …
Algebraic multigrid for discontinuous Galerkin discretizations of heterogeneous elliptic problems
We present a new algebraic multigrid (AMG) algorithm for the solution of linear systems
arising from discontinuous Galerkin (DG) discretizations of heterogeneous elliptic problems …
arising from discontinuous Galerkin (DG) discretizations of heterogeneous elliptic problems …
Enriched Galerkin methods for two-phase flow in porous media with capillary pressure
S Lee, MF Wheeler - Journal of Computational Physics, 2018 - Elsevier
In this paper, we propose an enriched Galerkin (EG) approximation for a two-phase
pressure saturation system with capillary pressure in heterogeneous porous media. The EG …
pressure saturation system with capillary pressure in heterogeneous porous media. The EG …
Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure
We consider an immiscible incompressible two-phase flow in a porous medium composed
of two different rocks so that the capillary pressure field is discontinuous at the interface …
of two different rocks so that the capillary pressure field is discontinuous at the interface …
A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows
M Vohralík, MF Wheeler - Computational Geosciences, 2013 - Springer
This paper develops a general abstract framework for a posteriori estimates for immiscible
incompressible two-phase flows in porous media. We measure the error by the dual norm of …
incompressible two-phase flows in porous media. We measure the error by the dual norm of …
Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method
We consider numerical simulation of two-phase flows in porous media using implicit
methods. Because of the complex features involving heterogeneous permeability and …
methods. Because of the complex features involving heterogeneous permeability and …
Bound-preserving discontinuous Galerkin method for compressible miscible displacement in porous media
H Guo, Y Yang - SIAM Journal on Scientific Computing, 2017 - SIAM
In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the
coupled system of compressible miscible displacement problems. We consider the problem …
coupled system of compressible miscible displacement problems. We consider the problem …