Sean Ryan Breckling

About Me

I’m currently a postdoctoral researcher at the University of Notre Dame. I was previously a postdoc researcher at the U.S. Air Force Institute of Technology (AFIT) –during the 2017-2018 academic year. I’m a fairly-recent graduate from the University of Nevada, Las Vegas. There I completed a Ph.D. in applied math under Dr. Monika Neda.

Apart from my research and teaching career, my main personal interests revolve around cycling –pun absolutely intended. Be it road or cyclocross racing, randonneuring, or simply commuting, it’s an infectious hobby and I’m always willing chat about it.

Research Interests

My research interests, broadly-stated, include topics in numerical analysis, scientific computing, and computational fluid dynamics. My work to date has centered largely around finite element methods, though I do have experience with the use and implementation of spectral methods. Some examples of research topics include techniques used to approximate complicated fluid flows, and how sensitive these models are to perturbations of their tuning parameters. The class of models I have the most experience with are large eddy simulation models (LES), which are widely applied in engineering and atmospheric sciences.

Published Research

S. Breckling, S. Shields, The Long-Time L^2 and H^1 Stability of Linearly Extrapolated Second-Order Time-Stepping Schemes for the 2D Incompressible Navier Stokes Equation, Applied Mathematics and Computation (Accepted 2018, In Print 2/1/2019).

S. Breckling, M. Neda, and T. Hill, A Review of Time Relaxation Methods, FLUIDS. 2017; 2,40. (Accepted 2017, Published 2017)

S. Breckling, and M. Neda Numerical study of the Navier–Stokes-α deconvolution model with pointwise mass conservation, International Journal of Computer Mathematics, pp 1-34 (Accepted 2016, Published 2017)

S. Breckling, M. Neda, and F. Pahlevani, A Sensitivity Study of the Navier-Stokes-α Model, (Preprint Published November 1, 2017, Computers and Mathematics With Applications)

Submitted Research and Drafts in Preparation

S. Breckling, [Regularizing an Extrapolated BDF2 Scheme for Incompressible Flows with Linear Time Relaxation], (Submitted)

S. Breckling, T. Kim, M. Neda, [The Joint Model Energy, Model Enstrophy Cascade of the Navier-Stokes-alpha Deconvolution Model] (Draft in preparation for submission in 11/18.)

S. Breckling, J. Fiordilino, S. Shields, [A note on the long-time stability of pressure solutions to the 2D Incompressible Navier-Stokes Equations] (Pre-print available, draft in preparation for submission in 10/18.)

Conference Proceedings

S. Breckling, P. Kachroo, P. Lakhanpal, M. Neda, [Numerical study of traffic flow models,] V International Conference of Industrial Engineering and Environmental Protections Proceedings, pp.217-222, 2015

Recent Conference Talks

2018 Finite Element Circus (Spring), University of Tennesee, Knoxville, TN. The Long-Time L^2 and H^1 Stability of Linearly Extrapolated Second-Order Time-Stepping Schemes for the 2D Incompressible Navier Stokes Equations

2017 APS Fluids Confrence, Denver, CO Regularizing an Extrapolated BDF2 Scheme for Incompressible Flows with Linear Time Relaxation

2017 Finite Element Circus (Fall), University of Maryland-Baltimore County, MD Regularizing an Extrapolated BDF2 Scheme for Incompressible Flows with Linear Time Relaxation

2017 JMM, Atlanta, GA A Numerical study of the Navier Stokes-α Deconvolution Model with Pointwise Mass Conservation

Education

Ph.D. in Applied Mathematics
University of Nevada, Las Vegas (2017)
Adviser: Prof. Monika Neda
Thesis: Numerical and Sensitivity Analyses of Navier-Stokes-α Models

B.S. in Mathematics
University of Wisconsin-Milwaukee (2010)