Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media

Jisheng Kou, Shuyu Sun

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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.
Original languageEnglish (US)
Pages (from-to)1674-1699
Number of pages26
JournalNumerical Methods for Partial Differential Equations
Volume30
Issue number5
DOIs
StatePublished - Mar 22 2014

ASJC Scopus subject areas

  • Computational Mathematics
  • Analysis
  • Applied Mathematics
  • Numerical Analysis

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