TY - JOUR
T1 - Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method
AU - Chung, Eric
AU - Efendiev, Yalchin R.
AU - Leung, Wing
AU - Ren, Jun
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2015/12/11
Y1 - 2015/12/11
N2 - In this paper, we develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media. We consider a coupled system consisting of a convection-dominated transport equation and a flow equation. We construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM) for a coupled system. In particular, multiscale basis functions are constructed based on some snapshot spaces for the pressure and the concentration equations and some local spectral decompositions in the snapshot spaces. The resulting approach uses a few multiscale basis functions in each coarse block (for both the pressure and the concentration) to solve the coupled system. We use the mixed framework, which allows mass conservation. Our main contributions are: (1) the development of a mass conservative GMsFEM for the coupled flow and transport; (2) the development of a robust multiscale method for convection-dominated transport problems by choosing appropriate test and trial spaces within Petrov-Galerkin mixed formulation. We present numerical results and consider several heterogeneous permeability fields. Our numerical results show that with only a few basis functions per coarse block, we can achieve a good approximation.
AB - In this paper, we develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media. We consider a coupled system consisting of a convection-dominated transport equation and a flow equation. We construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM) for a coupled system. In particular, multiscale basis functions are constructed based on some snapshot spaces for the pressure and the concentration equations and some local spectral decompositions in the snapshot spaces. The resulting approach uses a few multiscale basis functions in each coarse block (for both the pressure and the concentration) to solve the coupled system. We use the mixed framework, which allows mass conservation. Our main contributions are: (1) the development of a mass conservative GMsFEM for the coupled flow and transport; (2) the development of a robust multiscale method for convection-dominated transport problems by choosing appropriate test and trial spaces within Petrov-Galerkin mixed formulation. We present numerical results and consider several heterogeneous permeability fields. Our numerical results show that with only a few basis functions per coarse block, we can achieve a good approximation.
UR - http://hdl.handle.net/10754/592813
UR - http://www.mdpi.com/2079-3197/3/4/670
UR - http://www.scopus.com/inward/record.url?scp=85060841197&partnerID=8YFLogxK
U2 - 10.3390/computation3040670
DO - 10.3390/computation3040670
M3 - Article
SN - 2079-3197
VL - 3
SP - 670
EP - 686
JO - Computation
JF - Computation
IS - 4
ER -