Stochastic Analysis of Advection-Diffusion-Reaction Systems with Applications to Reactive Transport in Porous Media
EMSL Project ID
32297
Abstract
This project is funded by Department of Energy (DOE), Advanced Scientific Computing Research (ASCR) program. The mission of this project is to develop new uncertainty quantification capabilities and to apply the mathematical tools on decontamination of the DOE Hanford site, which has close relationship with EMSLâ??s mission and one of the four EMSLâ??s science themes: Geochemistry/biogeochemistry and subsurface science. The complexity of scientific and technical issues facing the 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. We are looking forward to employ the computational resources at EMSL to utilize the new predictive tools to solve the large scale grand challenge problems, in particular, the 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.
Project Details
Project type
Exploratory Research
Start Date
2009-01-12
End Date
2010-01-17
Status
Closed
Released Data Link
Team
Principal Investigator
Team Members
Related Publications
Lin G, and AM Tartakovsky. 2010. "Numerical studies of three-dimensional stochastic Darcy's equation and stochastic advection-diffusion-dispersion equation." Journal of Scientific Computing 43(1):92-117. doi:10.1007/s10915-010-9346-5
Lin G, DM Tartakovsky, and AM Tartakovsky. 2009. "Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids." Journal of Computational Physics, Volume 229, Issue 19, 20 September 2010, Pages 6995-7012
Tartakovsky AM. 2010. "Langevin Model for Reactive Transport in Porous Media." Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 82(2 PT 2):Art. No. 026302.