Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media
Type
ArticleAuthors
Kou, Jisheng
Sun, Shuyu

KAUST Department
Computational Transport Phenomena LabEarth Science and Engineering Program
Environmental Science and Engineering Program
Physical Science and Engineering (PSE) Division
Date
2014-03-22Online Publication Date
2014-03-22Print Publication Date
2014-09Permanent link to this record
http://hdl.handle.net/10754/564889
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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.Citation
Kou, J., & Sun, S. (2014). Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media. Numerical Methods for Partial Differential Equations, 30(5), 1674–1699. doi:10.1002/num.21817Sponsors
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 fundPublisher
Wileyae974a485f413a2113503eed53cd6c53
10.1002/num.21817