CMG Collaborative Research: Stochastic Domain Decomposition and Finite Elements for Modeling Subsurface Flow and Reactive Transport
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CSM: Mary F. Wheeler (PI), Raul Tempone (Co-PI), Shuyu Sun (Co-PI).
PE & G: Daniel Hill (Co-PI), Ding Zhu (Co-PI).
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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