Current Research

Novel Techniques in Numerical Simulations of Subsurface Hydrology

Working towards a PhD in Applied Mathematics and a PhD Minor in Hydrology, I'm studying under the supervision of Dr. Larry Winter and Dr. Shlomo Neuman. I have a particular fondness for numerical simulations and preforming those numerical simulations well.

My primary research interest is modeling ground water flow at a microscopic level. Working with Professor C. L. Winter, an affiliate of the Program in Applied Mathematics in the Hydrology department, we are simulating the movement of the fluid using high level computing.  Relating the flow  to explicit properties of the porous media, we are finding powerful relationships that will facilitate an understanding of how water moves in the ground beneath our feet.

Over the summer of 2011, I worked with Dr. Scott Painter and Dr. Carl Gable in the Computational Earth Science Group at Los Alamos National Labs to construct high quality meshes on stochastically generated discrete fracture networks. Combining tools from computational geometry, hydrology, and general applied mathematics we made great progress. Images and videos of the fully meshed networks will be available shortly.

Other academic interest of mine include numerical continuation methods for dynamical systems with bifurcations, numerical solutions to partial differential equations, scientific computing with python, and uncertainty quantification.

I firmly believe that one can never know too much Linear Algebra.

Publications

J.D.H., P. K. Smolarkiewicz, and C. L. Winter  (2012) Heterogeneities of Flow in Stochastically Generated Porous Media, Phys. Rev. E 86, 056701 doi:10.1103/PhysRevE.86.056701

 J.D.H., P. K. Smolarkiewicz, and C. L. Winter (2013), Pedotransfer functions for permeability: A computational study at pore scales, Water Resour. Res., 49, doi:10.1002/wrcr.20170.

Hyman, J. D. Gable, C. W. Painter, S. L. Automated Meshing of Stochastically Generated Discrete Fracture Networks (In Preparation)

Wang, C. M. Hyman J. D. Percus, A. Caflisch R. Parallel Tempering for the Traveling Salesman Problem International Journal of Modern Physics C, 2009, 20 (4), 539-556

Recent Talks

Summer 2012 3rd International EULAG conference, Loughborough,  England
        Title: Simulating Flow in Stochastically Generated Porous Media

Fall 2010 University of Arizona Applied Mathematics Second Year RTG conference:
       Title: Pores resolving simulation of Darcy flows

Fall 2010 University of Arizona Program in Applied Mathematics Brown Bag Series:
        Title: The Difficulties of numerically solving the Stokes Equations in a porous medium

Fall 2010 University of Arizona Graduate Mathematics Colloquium:
        Title: Parallel Tempering, Simulated Annealing, and the Traveling Salesman Problem

Spring 2010 University of Arizona's Applied Mathematics First Year RTG conference:
        Title: Modeling Stokes Flow in a Random Porous Media

Fall 2009 University of Arizona's Applied Mathematics First Year Lab Mini-symposium:
        Title: Oscillating fluid on a spinning rod with B. P. Berman and T. Sherman