Flow through heterogeneous porous media:
A stochastic variational multiscale framework

Baskar Ganapathysubramanian
Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
Cornell University

Abstract

Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these inherently multiscale phenomena. Such analysis is complicated by the limited information available to characterize the system. In this talk, I will discuss a recently developed strategy that comprehensively accounts for the twin issues of stochasticity and multiscale nature exhibited by such systems. The topics covered in this talk are:

1. A stochastic variational multiscale formulation to incorporate uncertain multiscale features,
2. Effective computational strategies to solve the resulting stochastic partial differential equations (SPDEs), and
3. A data driven strategy to incorporate limited experimental data into the stochastic analysis

A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Adaptive sparse grid collocation techniques are used to efficiently solve the resulting SPDEs. Strategies to incorporate the available (incomplete) information about the system properties are discussed. These strategies are based on ideas in manifold learning used in cognitive sciences and signal processing. Examples that illustrate the complete framework are presented. Extensions to the analysis, design and control of other physical processes that exhibit inherent stochasticity and multiscale character are discussed.

Thursday, February 7th
337 Towne Bldg.
2:00 – 3:00 p.m.