NCSU Differential Equations/Nonlinear Analysis Seminars

Location and Time: SAS 4201, Wednesday 15:00 -16:00

Organizers: Lorena Bociu, Patrick Combettes, Ryan Murray, and Khai T. Nguyen

NEXT TALK

Wednesday, Feb 19, 15:00-16:00, Zoom meeting: Link

Speaker: Sorin PoP, Hasselt University
Title: Non-equilibrium models for flow in porous media
Abstract: Porous media flows appear in several fields of highest societal relevance, such as environmental engineering, energy resources management, and flow through biological tissues. The underlying mathematical models can be expressed as (systems of) evolution equations, having a nonlinear and possibly degenerate character.

Next to the underlying conservation laws (mass, momentum, etc.), one typically assumes that the unknowns in such models (e.g. the capillary pressure and the saturation) are connected through an algebraic relationship, obtained under equilibrium conditions. For example, for a given medium and at a given saturation of the, say, wetting phase, the capillary pressure will always take the same value. Such an assumption is, however, invalidated by several experimental results reported in the literature. More precisely, as the solution satisfies a maximum principle, and some stability estimates in various energy norms, such equilibrium-based porous media flow models rule out the formation of so-called saturation overshoots, or of finger-like patterns, which are observed experimentally. This motivates extending the models commonly used in the literature by incorporating non-equilibrium effects like dynamic capillarity or hysteresis.

After providing the application background, in this presentation we briefly present some qualitative properties for such models (including the existence and uniqueness of weak solutions), and analyze various discretization schemes and linear iterative methods that are used to approximate the solution.

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