| CMG Collaborative Research:
Stochastic Domain Decomposition and Finite Elements for Modeling
Subsurface Flow and Reactive Transport
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Participants
CSM:
Mary F. Wheeler (PI), Raul Tempone (Co-PI), Shuyu Sun (Co-PI).
PE & G:
Daniel Hill (Co-PI), Ding Zhu (Co-PI).
Project Summary
The objective of this
proposal is to develop advanced numerical methods for modeling
complex subsurface hydrosystems to accurately simulate coupled
flow, transport and reaction processes over large space and
time scales, and which incorporate uncertainty. We propose
to couple two novel stochastic approaches—the random domain
decomposition method and the stochastic finite element method—with
mortar mixed finite element/mimetic finite difference methods
and/or discontinuous Galerkin for simulating coupled flow
and reactive processes.
The scope of the proposed
research necessitates an interdisciplinary research team involving
The University of Pittsburgh, The University of Texas at Austin,
and Los Alamos National Laboratory (LANL). The team consists
of applied mathematicians, computational scientists, and engineering
scientists in hydromechanics and stochastic partial differential
equations. While the investigators will share their expertise
in each problem area, National Science Foundation support
is requested only for researchers at the two universities.
Laboratory and field data and state of the art software platforms
will be available to the entire team from their participating
institutions and from their industrial collaborators.
The intellectual merits
of the resulting research include the following:
- Development of a methodology for dealing with heterogeneous
parameterizations in stochastic PDEs of elliptic, parabolic
and hyperbolic types;
- Study of variational approaches, mortar mixed finite
elements, mimetic finite differences, and discontinuous
Galerkin to study properties of stochastic PDEs whose
coefficients are defined on random subdomains;
- Investigation of two-scale stochastic modeling; namely,
development of an understanding of the relative importance
of two kinds of uncertainty in random domain decompositions:
large-scale uncertainty in the subdomain geometry, and
small-scale uncertainty in subdomain system parameters;
- Extension of the stochastic domain decomposition methodology
to two-phase flow and reactive transport in porous media
and derivation of effective upscaled parameters with random
system states defined on random subdomains;
- Development of software for simulating stochastic flow
nd transport processes. Validation and verification of
the stochastic mathematical models and their numerical
solutions developed in this project in the context of
several applications of interest to the environmental
community.
The broader impacts
resulting from the proposed activity include the following:
- Improvement of human life in general, since numerical
modeling contributes greatly to a sustainable management
and protection of water in the environment, which is of
paramount social and economic value;
- Establishment of an innovative approach for strengthening
the U.S. technical workforce through training of graduate
students, postdoctoral fellows, and possibly undergraduates;
- Educational and professional outreach and cross-disciplinary
training of future scientists and engineers through short
courses, conferences, workshops and vide and web-based
technologies;
- Dissemination of results to non-technical groups such
as Smartgirls and K-12 students through workshops and
meetings, e.g. Expanding Your Horizons.
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