Here is a summary of some of my current research projects/interests that I have pursued while working at NERSC.
There are a few applications for the porous media equations coupled with chemistry that our group is interested in investigating - carbon sequestration and flow of groundwater contaminants. I have been primarily focused on developing methods that will enable larger time-steps in our calculations, so we can simulate these flows out to 10's or 100's of computational years. The first component of that work was to implement a hybrid OpenMP/MPI programming, and investigate the performance of the PMAMR code on up to 49,152 processors. This work is described in a paper published in the Proceedings of the Cray User Group Meeting in 2011. Here are some plots illustrating both weak and strong scaling of the code with the hybrid model. Strong scaling is limited by the multigrid solver that is required for the implicit pressure calculations.
The equations of porous media are a highly nonlinear coupled system of PDEs. We currently solve these equations in an Implicit Pressure - Explicit Saturation form, with operator splitting for handling the capillary pressure present in the system. The method is second-order accurate and we are able to effectively capture the flow of fluids int he domain with this approach. However, the operator splitting that leads to a time-step restriction that is governed by the CFL condition. We are currently working on a second-order unsplit method for the two-phase, two-component porous media equations.
Flow of Groundwater Contaminants
There are various DOE sites where nuclear waste has been buried in tanks. Over time these tanks have developed cracks and some of the waste has trickled out into the subsurface. This creates a reactive flow that slowly moves toward the water table where the waste is eventually carried to the water supply. Simulations are useful in attempting to estimate the flow of the contaminants through the highly-heterogeneous medium. Many of the material properties are unknown throughout the simulation domain, so many different calculations must be done in order to properly characterize the flow behavior. This requires the ability to take larger time-steps than is currently possible, so the algorithm development I am doing now will be used for this application.
We want to develop an adaptive mesh refinement capability for a nonisothermal compositional model for simulating carbon sequestration. Our approach will be based on a sequential formulation in which we first solve for pressure and then advance conservation equations for composition and energy. The formulation is based on a thermodynamic characterization of phase behavior for nonisothermal system in which we perform an isenthalpic flash calculation based on minimizing the negative entropy of the system. This approach is based on theory developed in DEA van Odyck, JB Bell, et. al., Proc. Royal Soc. A, 465:523-549,2009. The image below was generated by George Pau, PhD, a staff scientist in the Earth Sciences Division at LBNL.