Research

My research revolves around the theme of modeling multi-scale phenomena in geophysics. In many aspects of geodynamics, small-scale, localized features greatly affect the large-scale dynamics, making for fascinating science and difficult computational problems. Currently I'm looking at a few applications and the development of computational methods to study these applications. Click on the pictures for more details (in some cases!)

Image of ??

Currently I've moved to Los Alamos National Laboratory, where I'm working on a post-doc with David Moulton on multiscale modeling in reactive flow in porous materials. More specifically, we're looking at hybrid models for carbon sequestration in geologic reservoirs. Lattice Boltzmann methods do a good job at modeling micro- and meso-scale features, but cannot scale to reservoir sizes. Darcy flow handles reservoir models well, but cannot handle the micro-scale features needed at the reaction front to accurately capture physics. We're looking at multilevel methods to bridge the gap between these two methods.

Image of XFEM Mode III crack

Networks of faults provide a tricky problem of representing discontinuous fields on complicated geometries. My thesis uses Nitsche- extended finite element methods that do not require the mesh to conform to the fault network by embedding the discontinuity in the basis function. The resulting methods allow for computation on even the nastiest of fault network geometries.

Image of Two-Phase Upscaled Flow

The dynamics of porous flow in highly heterogenous media are very dependent upon the small-scale heterogeneity. However, it is rarely computationally feasible to resolve the small scales while capturing the large simulation domains. Therefore, I've been working with colleagues to develop multilevel finite element upscaling methods to generate basis functions that respect sub-grid-scale heterogenaity.

Image of a Shear Zone

Shear zones are perhaps the most obvious examples of localized deformation in geodynamics. I've been developing models of viscoelastic shear zones which localize as a result of grain size heterogeneity, demonstrating the importance of rheological considerations in localization. These models exhibit a wide range of dynamical phenomena, from periodic, catastrophic, earthquake-like events to multiple, distributed shear localizations.

Image of Shear Zone under the San Andreas

The above work in shear zones has led to an interest in the interaction of the mantle and crust below slip-strike faults. The relative strengths of the upper mantle and lower crust is still in question, and this has interesting implications for the interaction of faults and viscous shear zones in the mantle below.