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Fifth Year PhD Student
Energy Science & Engineering Department
Monday, October 3, 2022
12:30 PM - 1:20 PM
This meeting is in Room 104 and can be viewed in Room 014
In engineering applications involving multiscale systems, it is often valuable to understand coarse-scale, or average, physical behaviors and how they are affected by intricate fine-scale variations. As such, macroscopic partial differential equations can be used to accurately capture the large-scale dynamics of a system and efficiently model physical processes across multiple scales. These equations can be systematically generated through rigorous upscaling techniques, which provide a priori error estimates and conditions under which the equations are valid (i.e., applicability conditions). However, the analytical derivations required in upscaling techniques are time-consuming, error-prone, and become quickly intractable for complex, multi-physical systems. To ease these complications, we propose a method of automatic upscaling through symbolic computation. By automating the required analytical derivations, we democratize the utilization of upscaling techniques in practical applications and enable multiscale model development in a feasible amount of time (i.e., seconds to minutes) with no requirements in analytical tractability, nor specialized expertise in mathematical model formulation. In this presentation, we give an overview of our software prototype, Symbolica, and demonstrate its functionality by upscaling various advective-diffusive-reactive systems. We then discuss our recently developed upscaling strategy for extending the applicability of upscaled models, which has enhanced Symbolica's automation capabilities and facilitated scientific discovery. Finally, we discuss a complex application of Symbolica to study heat transfer and thermal runaway in Lithium ion battery packs.
Kyle Pietrzyk is a fifth year PhD candidate working with Prof. Ilenia Battiato in the Energy Science and Engineering Department at Stanford University. His research involves multiscale modeling for reactive mass transport in porous media and energy applications. Specifically, Kyle's work pertains to the development and application of Symbolica, a symbolic computational code that automates rigorous multiscale model development procedures (e.g., upscaling methods) for systems of realistic complexities. He received the Stanford Graduate Fellowship for Science and Engineering (2018), the Henry J. Ramey, Jr. Fellowship Award from the Energy Resources Engineering Department at Stanford University (2022), and works as the DEI Coordinator for the Stanford Doerr School of Sustainability (2022).
Reference and Related Papers:
K. Pietrzyk, S. Korneev, M. Behandish, and I. Battiato, “Upscaling and automation: Pushing the boundaries of multiscale modeling through symbolic computing,” Transp. Porous Media, vol. 140, pp. 313–349, 2021.
K. Pietrzyk and I. Battiato, “Automated symbolic upscaling: Model generation for extended applicability regimes, part 1,” (Submitted to Water Resour. Res.), 2022.
K. Pietrzyk and I. Battiato, “Automated symbolic upscaling: Model generation for extended applicability regimes, part 2,” (Submitted to Water Resour. Res.), 2022.
I. Battiato, P. T. Ferrero V, D. O’Malley, C. T. Miller, P. S. Takhar, F. J. Valdes-Parada, and B. D. Wood, “Theory and applications of macroscale models in porous media,” Transp. Porous Media, vol. 130, pp. 5–76, 2019.