Sanghyun Lee
Associate Professor, Department of Mathematics, Florida State University
Appointments
- Fall 2023–present Associate Professor, Department of Mathematics, Florida State University
- Fall 2017–Summer 2023 Assistant Professor, Department of Mathematics, Florida State University
Joint Appointments
- Spring 2026–Spring 2028 Global Joint Appointment Faculty, Department of Mathematics, Kyungpook National University, South Korea
- Spring 2024–present Associate, Institute for Data Science, Florida State University [link]
- Spring 2018–present Associate, Geophysical Fluid Dynamics Institute, Florida State University [link]
Computation for multiphysics PDEs
Physics-preserving numerical methods and scientific machine learning for flow, transport, fracture, and subsurface systems.
News
2026
Ph.D. DefenseYi-Yung Yang defended his Ph.D. dissertation
Title: Physics-Preserving Enriched Galerkin Methods for Hyperbolic and Coupled Flow–Transport Problems
Local conservation, maximum-principle preservation, and entropy stability are crucial for producing physically meaningful numerical simulations of hyperbolic and coupled flow–transport problems. In this dissertation, we develop physics-preserving enriched Galerkin finite element methods for these problems. We first study coupled Darcy flow and linear transport problems in porous media, where locally conservative enriched Galerkin flow discretizations are used to provide reliable velocity fields for transport simulations. To prevent nonphysical undershoots and overshoots, we incorporate flux-corrected transport techniques into the enriched Galerkin framework so that the numerical concentration satisfies a discrete maximum principle. Next, we study nonlinear scalar hyperbolic conservation laws, for which weak solutions may not be unique and entropy stability is needed to select the physically admissible solution. To address this issue, we develop bound-preserving and entropy-stable enriched Galerkin schemes by using algebraic flux correction and monolithic convex limiting techniques. Finally, we apply the proposed framework to enhanced geothermal energy modeling and develop a three-temperature local thermal nonequilibrium model that distinguishes the thermal behavior of injected fluid, resident fluid, and the solid matrix. Numerical experiments validate the proposed methods for locally conservative flow, bound-preserving transport, entropy-stable nonlinear conservation laws, and geothermal flow and heat-transfer simulations.
PresentationLee's group presented at Spring 2026 FEM Circus
Postdoc Dr. K. Chawla and Ph.D. student Y. Yang presented their work.
Ph.D. DefenseRuth Lopez defended her Ph.D. dissertation
PaperA joint paper with S. Moon and D. Park was published in JCAM
A Machine Learning and Finite Element Framework for Inverse Elliptic PDEs via Dirichlet-to-Neumann Mapping
D. Park, S. Lee, S. Moon, Journal of Computational and Applied Mathematics.
D. Park, S. Lee, S. Moon, Journal of Computational and Applied Mathematics.
PresentationLee's group presented at the 4th Southeast ACM Student Workshop
Postdoc Dr. K. Chawla and Ph.D. students S. M. Lee, J. Valyou, and Y. Yang presented their work.
PresentationLee presented at the FSU–NC State PDE Workshop
PresentationLee presented at the NACS Seminar, Rice University
2025
PresentationLee presented at Aramco
PaperOur paper was accepted for publication in the International Journal for Numerical and Analytical Methods in Geomechanics
The paper is co-authored with Jihoon Kim and Mary Wheeler, and the title is The von Neumann Stability Analysis of the Fixed-Stress Schemes in Poroelastodynamics.
PaperOur paper was accepted for publication in Computers and Mathematics with Applications
The paper is co-authored with Seungmin Lee, and the title is Convergence and Numerical Simulations of the Continuous Data Assimilation for Biot’s Poroelasticity.
PaperOur paper was accepted for publication in the International Journal for Numerical and Analytical Methods in Geomechanics
The paper is co-authored with Hemanta Kunwar and Son-Young Yi, and the title is Non-intrusive Global-local Method for Poroelasticity Problems with Localized Pressure Effects.
PresentationLee presented at the ARMA Hydraulic Fracturing Seminar
PresentationLee presented at the CCAM Seminar, Purdue University
Organizer/PresentationLee co-organized a minisymposium and presented at the SIAM Geosciences Conference
Organizer/PresentationLee co-organized the 8th Biot Conference and presented a talk
The program is available here: Program.
PresentationKapil Chawla and Jonathan Valyou presented at the 12th Graduate Student Conference at Clemson University
The program is available here: Program.
PaperOur paper was accepted for publication in Journal of Computational Physics
The paper is co-authored with Ryuou Hu, Sanjeeb Poudel, and Feng Bao from Florida State University, and it is titled Ensemble Score Filter for Data Assimilation of Two-Phase Flow Models in Porous Media. The arXiv version is available below.
PaperOur paper was accepted for publication in Journal of Computational Physics
The paper is co-authored with Yi-Yung Yang and Dmitri Kuzmin (TU Dortmund), and it is titled Bound-preserving and Entropy Stable Enriched Galerkin Methods for Nonlinear Hyperbolic Equations. The arXiv version is available below.
PresentationLee presented at MoST 2025, Moselle Valley, Germany
New MemberKapil Chawla joined our group at FSU
Kapil Chawla received his Ph.D. from Indiana University in 2025. His Ph.D. advisor is R. Temam. Kapil is funded by the DOE Earthshot program and will work on machine-learning-based multiscale methods. Welcome!