TY - JOUR
T1 - Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media
AU - Kou, Jisheng
AU - Sun, Shuyu
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Contract grant sponsor: National Natural Science Foundation of China; contract grant number: 11301163Contract grant sponsor: Key Project of Chinese Ministry of Education; contract grant number: 212109Contract grant sponsor: KAUST research fund
PY - 2014/3/22
Y1 - 2014/3/22
N2 - Discontinuous Galerkin methods with interior penalties and upwind schemes are applied to the original formulation modeling incompressible two-phase flow in porous media with the capillary pressure. The pressure equation is obtained by summing the discretized conservation equations of two phases. This treatment is very different from the conventional approaches, and its great merit is that the mass conservations hold for both phases instead of only one phase in the conventional schemes. By constructing a new continuous map and using the fixed-point theorem, we prove the global existence of discrete solutions under the proper conditions, and furthermore, we obtain a priori hp error estimates of the pressures in L 2 (H 1) and the saturations in L ∞(L 2) and L 2 (H 1). © 2014 Wiley Periodicals, Inc.
AB - Discontinuous Galerkin methods with interior penalties and upwind schemes are applied to the original formulation modeling incompressible two-phase flow in porous media with the capillary pressure. The pressure equation is obtained by summing the discretized conservation equations of two phases. This treatment is very different from the conventional approaches, and its great merit is that the mass conservations hold for both phases instead of only one phase in the conventional schemes. By constructing a new continuous map and using the fixed-point theorem, we prove the global existence of discrete solutions under the proper conditions, and furthermore, we obtain a priori hp error estimates of the pressures in L 2 (H 1) and the saturations in L ∞(L 2) and L 2 (H 1). © 2014 Wiley Periodicals, Inc.
UR - http://hdl.handle.net/10754/564889
UR - http://doi.wiley.com/10.1002/num.21817
UR - http://www.scopus.com/inward/record.url?scp=84905106667&partnerID=8YFLogxK
U2 - 10.1002/num.21817
DO - 10.1002/num.21817
M3 - Article
VL - 30
SP - 1674
EP - 1699
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
SN - 0749-159X
IS - 5
ER -