Shriram Srinivasan: Pressure dependent viscosity and reduced-order modelling in flow through porous media

Abstract: 

In this talk, I aim to provide a connected narrative of  two computational challenges that beset problems involving flow through porous media. First I shall describe the physical implications of constitutive theories that allow the viscosity to depend on the pressure, leading upto the computational challenges of it. We shall see that such theories are but one instance of a general class of implicit constitutive theories in which the kinematics is expressed as a function of the stresses, an inversion of the well-entrenched practice that expresses the stress as a function of the kinematics.

Then we turn to the computational issues engendered by heterogeneity of porous media, seen through a  simple linear PDE. I briefly discuss two upscaling methods for the standard parabolic  PDE with a heterogeneous diffusion coefficient, both based on locally one-dimensional splitting schemes.The first involves the Schur complement to coarsen the system, while the second is a reformulation of the PDE in terms of the flux. The flux formulation is connected  to constitutive theory and it ties the subject matter back to the first half of the talk.