Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media
KAUST DepartmentComputational Transport Phenomena Lab
Physical Sciences and Engineering (PSE) Division
Environmental Science and Engineering Program
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AbstractDiscontinuous 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.
SponsorsContract 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