|Dept.||The Univ. of Texas at Austin|
* 세미나 장소 : 25동 114호
The talk presents the numerical simulations for bouncing fluid and solid fracture propagation to illustrate the potential of computational mathematics, which perform as a central and essential role to understand science these days.
The first part will focus on the fascinating phenomenon of a leaping shampoo stream, the Kaye effect. This is a property of non-Newtonian fluid, which was first described by Alan Kaye in 1963. It manifests itself, when a thin stream of non- Newtonian fluid is poured into a dish of the fluid. As pouring proceeds, a small stream of liquid occasionally leaps upward from the heap and bounces. We have studied a mathematical model and algorithm to show that the jet slides and bounces on a lubricating air layer and to find the range of parameters to observe the Kaye effects. In this context we propose a modified projection method for Navier-stokes equation with open boundary, level set method for free boundary and adaptivity.
Next, we propose a computational modeling of the effects of the formation and growth of the proppant-filled hydraulic fractures in poroelastic media to the oil and gas production and CO2 sequestration in reservoir by using phase-field approach. This technique to produce gas from shale has brought enormous impact in the whole world. The phase field model is based on Biot system and employs fixed stress iteration to couple flow and mechanics. Enriched Galerkin finite element discretization is applied to flow and transport systems to ensure local and global mass conservativeness for miscible displacement problems.
This is a joint work with Andrea Bonito, Jean-Luc Guermod, Andro Mikelic, Young-Ju Lee, Mary F. Wheeler, and Thomas Wick.