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Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two‐phase flow in porous media
Author(s) -
Kou Jisheng,
Sun Shuyu
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21817
Subject(s) - mathematics , discretization , conservation of mass , compressibility , porous medium , discontinuous galerkin method , partial differential equation , flow (mathematics) , mathematical analysis , incompressible flow , conservation law , galerkin method , capillary pressure , finite element method , porosity , geometry , mechanics , thermodynamics , physics , geology , geotechnical engineering
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 inL 2 ( H 1 ) and the saturations inL ∞ ( L 2 ) andL 2 ( H 1 ) . © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1674–1699, 2014