WHAT DID THE 2011 EARLY CAREER AWARD ALLOW YOU TO DO?
There’s a famous expression attributed to Albert Einstein. He said that mathematical models should be as simple as possible, but no simpler than necessary to explain the answer to the questions you are asking.
The U.S. Department of Energy’s Early Career Research Program Award (ECRP) enabled us to develop mathematical methods for finding simple models. These models have potential for improving the accuracy and efficiency of computer codes in a wide variety of scientific applications, including carbon dioxide sequestration in subsurface, fate and transport of contaminants in aquifers, and the battery design.
For example, we proposed new mathematical models for several fundamental processes, including the interactions of several fluids and spreading of dissolved species in porous materials.
My postdocs and I developed methods to explore multiphase (gas, solid, and/or liquid) flows at extremely small scales.
For the transport of dissolved species, we proposed a method allowing a separate (and more accurate) modeling of the coupled mechanical and diffusive mixing processes on a large scale.
This method significantly improved the accuracy of transport models without increasing the overall computational cost.
The ECRP allowed me to work on problems that motivated research of many mathematicians and physicists. I’ve applied the lessons learned as I continue my research at the university level.
Alexandre M. Tartakovsky is a professor in the Department of Civil and Environmental Engineering at the University of Illinois at Urbana-Champaign and a laboratory fellow at the Pacific Northwest National Laboratory.
SUPPORTING THE DOE SC MISSION:
The Early Career Research Program provides financial support that is foundational to early career investigators, enabling them to define and direct independent research in areas important to DOE missions. The development of outstanding scientists and research leaders is of paramount importance to the Department of Energy Office of Science. By investing in the next generation of researchers, the Office of Science champions lifelong careers in discovery science.
For more information, please go to the Early Career Research Program.
THE 2011 PROJECT ABSTRACT:
New Dimension Reduction Methods for Multi‐scale Nonlinear Phenomena
This project will develop a new dimension‐reduction method for complex, multiscale, non‐linear problems and design scalable, communication‐minimizing algorithms for the implementation of this method on leadership‐class computers. Many mathematical models of natural and/or engineered systems are multiscale and nonlinear and have a common feature: Their discrete approximations are systems of ordinary differential equations (ODEs), which can contain an enormous number of unknowns. Direct simulation of these models can be extremely expensive.
The dimension reduction methods will provide a rigorous mathematical foundation for approximating large systems of ODEs with models containing a much smaller number of unknowns. By doing this, the new method will address computational challenges posed by large‐size ODE models. These outcomes would constitute a breakthrough in multiscale modeling with a strong potential for significant advances in various engineering and science applications.
P. de Anna, T. Le Borgne, M. Dentz, A.M. Tartakovsky, D. Bolster, and P. Davy, “Flow intermittency, dispersion, and correlated continuous time random walks in porous media.” Physical Review Letters 110, 184502 (2013). [DOI: 10.1103/PhysRevLett.110.184502]
A.M. Tartakovsky and A. Panchenko, “Pairwise force smoothed particle hydrodynamics model for multiphase flow: surface tension and contact line dynamics.” Journal of Computational Physics 305, 1119 (2016) . [DOI:10.1016/j.jcp.2015.08.037]
D.A. Barajas-Solano and A.M. Tartakovsky, “Hybrid multiscale finite volume method for advection-diffusion equations subject to heterogeneous reactive boundary conditions.” Multiscale Modeling & Simulation 14, 1341 (2016). [DOI: 10.1137/15M1022537]
Additional profiles of the Early Career Research Program award recipients can be found on the Early Career Program Page.
The Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, please visit www.energy.gov/science.
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