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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, May 29, 2020 - 12:00 to 12:50

Location:

ZOOM

Event Link:

Local Speaker:

Abstract:

This presentation will be given online by zoom, with the zoom link sent to the AMC seminar list. Participants interested in viewing should sign up for that list (see AMC Seminar website).

ABSTRACT: In this presentation we consider a model for freezing in porous media. Ideally, such a model would account for the balance of mass, momentum, and energy in the media and for all the coupled processes, at all the relevant scales. However, the computational complexity in modeling these relations at their natural scales is enormous. The challenge is to combine these multiple relations and the multiple scales at which these occur in an optimal way without reducing the overall model precision. At the Darcy scale, the single-phase fluid flow and the consequential deformation in porous media is described by the classical Biot system which couples the conservation of mass with the balance of momentum in the fluid and solid parts of the porous media. Next, the ice-water model we consider is the classical Stefan problem and we further review the model of frost heave due to Miller and O'Neill.

In our approach, we consider the coupling of some of these models at a lower scale. In particular, we consider the computationally inexpensive, but intuitive, network models to analyse the three phases: water, grain (porous matrix), and ice. In this talk, initial results on each of these models will be presented. Our ultimate goal is to apply our models to study the frost heave, and the impact of thawing of the permafrost in the Arctic on the landscape features such as pingos.

(This presentation is the public part of Naren Vohra's MS oral exam. All those not on the MAC seminar list can contact Nikki Sullivan for zoom link.)

Abstract Link: