Research Projects

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

Principal investigators

Prof. Dr. Siddhartha Mishra, Seminar for Applied Mathematics, ETH Zurich
Giuseppe Coclite, University of Bari
Kenneth Karlsen, CMA, University of Oslo
Nils Henrik Risebro, CMA, University of Oslo

Start date: 11.05.2008

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

G. M. Coclite, S. Mishra, K. H. Karlsen and N. H. Risebro. Convergence of vanishing viscosity approximations for a multi-dimensional triangular systems of conservation laws, Boll. Unione. Mat. Ital., 9/2 (2009), pp. 275-284
G. M. Coclite, S. Mishra and N. H. Risebro. Convergence of an Engquist-Osher scheme for a multi-dimensional triangular systems of conservation laws, Mathematics of Computation, 79/269 (2010), pp. 71-94, doi
G. M. Coclite, K. H. Karlsen, S. Mishra and N. H. Risebro. A hyperbolic-elliptic model of two-phase flow in porous media - existence of entropy solutions, Int. J. Num. Anal. Model, 9/3 (2012), pp. 562-583, SAM Report 2011-06

Funding

RCN funding under the center of excellence initiative.

Contact

Siddhartha Mishra