Mathematical study and robust numerical methods for multi-phase flows in multi-dimensional porous media

Description

The project focuses on the mathematical study of the equations that govern multi-phase flow in a multi-dimensional porous medium. The equations are non-linear system consisting of an elliptic equation for the pressure and a hyperbolic equation for the saturation. We have developed approximate models for two-phase flow that are well-posed. Robust numerical methods to simulate multi-phase flow are also being developed. Ongoing research focuses on the derivation of more physically realistic models and on extending the results to three phase flow.

Publications / Preprints or SAM-Reports

• Convergence of vanishing viscosity approximations for a multi-dimensional triangular systems of conservation laws, G. M. Coclite, K. H. Karlsen, S. Mishra and N. H. Risebro, Bulletin of UMI, 9 (2), 2009, 275-284.
• Convergence of an Engquist-Osher scheme for a multi-dimensional triangular systems of conservation laws, G. M. Coclite, S. Mishra and N. H. Risebro, Mathematics of Computation, 79 (269), 71-94, 2010
• A hyperbolic-elliptic model of two-phase flow in porous media - Existence of entropy solutions, G. M. Coclite, K. H. Karlsen, S. Mishra and N. H. Risebro, SAM report 2011-06.

Funding

RCN funding under the center of excellence initiative.

Contacts

S. Mishra