Funding DOE/PNNL - DE-FG02-07ER25818

Stochastic Analysis of Advection-Diffusion-Reactive Systems with Applications to Reactive Transport in Porous Media

In collaboration with: Guang Lin, PhD (PNNL)

The complexity of scientific and technical issues facing the Department of Energy (DOE) requires the development of new predictive capabilities for physical, chemical, and biological processes, many of which are fundamentally uncertain. We propose to develop a new mathematical and numerical framework for tracking parametric uncertainty in simulations of nonlinear advection-diffusion-reaction phenomena in highly heterogeneous environments. Although such systems occur in a variety of applications, we will focus on reactive transport in natural porous media, with an application to environmental stewardship and decontamination of the DOE Hanford site.

Our technical objectives are: (i) to develop multi-element generalized Polynomial Chaos representations and obtain stochastic solutions using Galerkin and collocation procedures, (ii) to develop robust adaptive criteria for h ? p refinement of the random space, (iii) to develop deterministic equations for statistical moments and/or full PDFs of concentration of reactive species, and (iv) to increase the accuracy and the range of applicability of these approaches by means of Random Domain Decompositions. The proposed work will have significant and broad impact as it will contribute towards a rigorous foundation of data assimilation and stochastic modeling of advection-reaction-diffusion systems. It will establish a composite error bar in systems of great interest to DoE that goes beyond numerical accuracy and includes uncertainties in operating conditions, the physical parameters, and the domain. In addition, stochastically simulated responses can provide complete sensitivity analysis that could potentially guide experimental work and dynamic instrumentation. Thus, the new approach will affect fundamentally the way we design new experiments and the type of questions that we can address, while the interaction between simulation and experiment will become more meaningful and more dynamic.

Publications

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