Numerical analysis of a non equilibrium two-component two-compressible flow in porous media
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
Date
2013-09-17Online Publication Date
2013-09-17Print Publication Date
2014Permanent link to this record
http://hdl.handle.net/10754/562951
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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.Citation
Saad, B., & Saad, M. (2014). Numerical analysis of a non equilibrium two-component two-compressible flow in porous media. Discrete & Continuous Dynamical Systems - S, 7(2), 317–346. doi:10.3934/dcdss.2014.7.317Sponsors
This work was partially supported by GNR MOMAS.ae974a485f413a2113503eed53cd6c53
10.3934/dcdss.2014.7.317