10-02-2019 | Jared Crean: Nonlinearly Stable High-Order Methods for Hyperbolic Partial Differential Equations

Nonlinearly Stable High-Order Methods for Hyperbolic Partial Differential Equations

Speaker: Jared Crean, NIA Visitor
Date: Wednesday, Oct. 2, 2019
Time: 10:30 a.m.
Location: NASA/LaRC, Bldg. 1268A, Room 2120
Sponsor: Mark Carpenter, NASA/LaRC

Jared is a doctoral candidate at Rensselaer Polytechnic Institute in the Department of Mechanical, Aerospace and Nuclear Engineering in Troy, New York. His supervisor and mentor is Dr. Jason Hicken. His thesis is entitled “Advances in Computational Fluid Dynamics with Discrete Entropy Properties.” He holds a Mechanical Engineering degree with a minor in Pure and Applied Mathematics from Stevens Institute of Technology in Hoboken, New Jersey. In 2018, he tied for 1st prize for the AIAA Multi-Disciplinary Optimization Student Paper Competition. He is also the recipient of the Edwin A. Stevens Scholarship and Stevens Presidential Scholarship, both four-year merit-based scholarships for academic performance.

This talk will discuss nonlinearly stable high-order methods for hyperbolic partial differential equations. Several topics will be discussed, including summation-by-parts operators, connections to discontinuous Galerkin methods, and entropy-stable shock capturing. Additionally, a recently developed a-posteriori r-adaptation method will be presented, which minimizes entropy dissipation to produce a mesh that better resolves the solution. This method is particularly beneficial when discontinuities are present.