Numerical analysis of a non equilibrium two-component two-compressible flow in porous media

Bilal Mohammed Saad, Mazen Naufal B M Saad

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We propose and analyze a finite volume scheme to simulate a non equilibrium two components (water and hydrogen) two phase flow (liquid and gas) model. In this model, the assumption of local mass non equilibrium is ensured and thus the velocity of the mass exchange between dissolved hydrogen and hydrogen in the gas phase is supposed finite. The proposed finite volume scheme is fully implicit in time together with a phase-by-phase upwind approach in space and it is discretize the equations in their general form with gravity and capillary terms We show that the proposed scheme satisfies the maximum principle for the saturation and the concentration of the dissolved hydrogen. We establish stability results on the velocity of each phase and on the discrete gradient of the concentration. We show the convergence of a subsequence to a weak solution of the continuous equations as the size of the discretization tends to zero. At our knowledge, this is the first convergence result of finite volume scheme in the case of two component two phase compressible flow in several space dimensions.
Original languageEnglish (US)
Pages (from-to)317-346
Number of pages30
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume7
Issue number2
DOIs
StatePublished - Sep 17 2013

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

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