TY - JOUR

T1 - Numerical analysis of a non equilibrium two-component two-compressible flow in porous media

AU - Saad, Bilal Mohammed

AU - Saad, Mazen Naufal B M

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was partially supported by GNR MOMAS.

PY - 2013/9/17

Y1 - 2013/9/17

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/562951

UR - http://aimsciences.org//article/doi/10.3934/dcdss.2014.7.317

UR - http://www.scopus.com/inward/record.url?scp=84888168423&partnerID=8YFLogxK

U2 - 10.3934/dcdss.2014.7.317

DO - 10.3934/dcdss.2014.7.317

M3 - Article

SN - 1937-1632

VL - 7

SP - 317

EP - 346

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 2

ER -