Date:

Monday, September 17, 2007,
11:00 am - 12:00 pm.

Place:

Mathematics Conference Room 626, UCD Building, 1250 14th St., Denver.

Speaker:

Ruben Juanes.

Affiliation:

Department of Civil and Environmental Engineering, Massachusetts Institute of Technology.

Title:

Variational multiscale methods for heterogeneous porous media flows.

Abstract:

We present a variational multiscale mixed finite element method for the solution of Darcy flow in porous media, in which both the permeability field and the source term display a multiscale character. The formulation is based on a multiscale split of the solution into coarse and subgrid scales. This decomposition is invoked in a variational setting that leads to a rigorous definition of a (global) coarse problem and a set of (local) subgrid problems. One of the key issues for the success of the method is the proper definition of the boundary conditions for the localization of the subgrid problems. We identify a weak compatibility condition that allows for subgrid communication across element interfaces, something that turns out to be essential for obtaining high-quality solutions. We also remove the singularities due to concentrated sources from the coarse-scale problem by introducing additional multiscale basis functions, based on a decomposition of fine-scale source terms into coarse and deviatoric components. The method is locally conservative and employs a low-order approximation of pressure and velocity at both scales. We illustrate the performance of the method on several synthetic cases, and conclude that the method is able to capture the global and local flow patterns accurately.

Short Bio:

Ruben Juanes is assistant professor of Civil and Environmental Engineering at MIT. Before joining the MIT faculty in 2006, he was an acting assistant professor in Petroleum Engineering at Stanford University, and an assistant professor in Petroleum and Geosystems Engineering at UT Austin. He holds MS (1999) and PhD (2003) degrees in Civil and Environmental Engineering from the University of California at Berkeley. His research is geared toward the understanding, modeling, simulation and quantitative prediction of complex geophysical systems, with special application to petroleum reservoir engineering, groundwater hydrology, geological CO2 sequestration and gas hydrates in ocean sediments. He develops analytical theories and numerical techniques that capture the multiscale phenomena ubiquitous to flow and transport in the environment.