Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, June 5, 2015 - 12:00 to 13:00

Location:

GLK 113

Event Link:

Guest Speaker:

Timothy Costa

Abstract:

The simulation of flow and transport processes in a complex porous

media at pore-scale is prohibitively expensive for most real applications.

Two widely used alternatives to the simulation of Navier-Stokes at the

pore-scale are to (i) upscale to core-scale and simulate a Darcy or

non-Darcy model which averages geometric properties through a conductivity

tensor, and to (ii) construct a pore-network model which relies on

approximation of the pore-scale geometric features into pores and throats

along with a relationship between throat length, radius, and conductivity. A

better approach is to combine these three representations of a porous media

into a multi-scale simulation framework. An additional concern in simulating

pore-scale flow stems from geometric uncertainty, both from uncertainty in

imaging as well as when there is porescale modification due to, e.g., hydrate formation or biofilm growth.

This results in pore-scale problems posed on stochastic domains, an area of

numerical analysis that has received increasing attention in recent years.

In this talk we present a three-scale simulation framework for flow in

porous media, which, at the pore-scale, relies on accurate computations of

conductivity. At the pore-scale we model geometric uncertainty through an

immersed boundary representation of hydrate formation or biofilm growth.

Computing statistics of the quantity of interest, the conductivity, in the

setting of random domains is shown to be a considerable computational

undertaking, and we explore a reduced order model for conductivity in the

presence of growth within the fluid domain, which dramatically reduces the

computational complexity of the three-scale solver.

Part of this work is joint with M. Peszynska, A. Trykozko, K. Kennedy, M. Prodanovic, and D. Wildenschild.