Collaborative Research: Error Estimation, Data Assimilation and Uncertainty Quantification for Multiphysics and Multiscale Processes in Geological Media

(funded by NSF)

The application of high performance computing to model subsurface processes occurring over multiple spatial and temporal scales is a science grand challenge that has important implications to society at large. Research on this grand challenge is at the confluence of advanced mathematics, computer science, fluid and solid mechanics and applied probability and statistics. We are engaging in a fresh new perspective by investigating and formulating rigorous error estimators for the numerical schemes employed to model multiphysics, multiscale processes in subsurface media. These error estimators, when coupled with advanced computational methods, can significantly speed up the task of uncertainty assessment and feedback control of subsurface processes.

We are also developing a uncertainty quantification scheme that will utilize the error estimators and rigorous quantification of prior geologic uncertainty. Underlying the computational and uncertainty quantification schemes will be a computer framework that rigorously takes into account the dynamic and complex communication and coordination patterns resulting from multiphysics, multinumerics, multiscale and multidomain couplings. In addition, we will investigate realistic physical models such a carbon sequestration in saline aquifers with real field data from the Cranfield Mississippi demonstration site. The ultimate transformative goal is to achieve predictive and decisional simulations, in which engineers reliably predict, control, and manage human interaction with geosystems.