Title: Discretely Entropy Stable High Order Methods for Nonlinear Conservation Laws
Speaker: Jesse Chan, Assistant Professor, Rice University
Date: Wednesday, May 16, 2018
Location: NASA/LaRC, B1268-R1069
Host: Mark Carpenter, NASA/LaRC
Abstract: High order methods offer several advantages in the approximation of solutions of nonlinear conservation laws, such as improved accuracy and low numerical dispersion/dissipation. However, these methods also tend to suffer from instability in practice, requiring filtering, limiting, or artificial dissipation to prevent solution blow up. Provably stable finite difference methods based on summation-by-parts (SBP) operators and a concept known as flux differencing address this inherent instability by ensuring that the solution satisfies a semi-discrete entropy inequality. In this talk, we discuss how to construct discretely entropy stable high order discontinuous Galerkin methods by generalizing entropy stable finite difference schemes using discrete L2 projection matrices and “decoupled” SBP operators. Extensions to curved meshes will be also discussed, and numerical experiments for the one and two-dimensional compressible Euler equations confirm the semi-discrete stability and high order accuracy of the resulting methods.
Biography: (from Rice University article – April, 2018)
Jesse Chan planned to major in English and philosophy when he arrived at Rice University in 2004 but encountered an unexpected detour his freshman year in the form of computational and applied mathematics (CAAM). “It even surprised me. I took a class with Prof. Timothy Redl, who’s now at the University of Houston Downtown). It was CAAM 210, Introduction to Engineering Computation. It resonated, and I decided to move in a different direction,” said Chan, assistant professor of CAAM, who joined the Rice faculty in 2016. “I have several different research interests, but what they have in common is a focus on simulating physical phenomena. There are multiple aspects of this field that I’m interested in, from the theoretical to the practical.” he said. Chan’s research interests include high-order discontinuous Galerkin methods for problems in wave propagation and fluid dynamics, as well as efficient, high-performance implementations of numerical methods on many-core and GPU (graphics processing units) architectures.
“You can think of a regular computer CPU as a single Corvette. It’s fast and powerful, but there’s only one. With GPUs, it’s more like a fleet of tractors. They’re slower individually, but harnessed together they can sweep through large tasks more efficiently,” he said. Chan earned a B.A. in CAAM from Rice in 2008, and an M.A. and Ph.D. in Computational Science, Engineering and Mathematics (C.S.E.M.) from the Institute for Computational Engineering and Sciences at the University of Texas in Austin in 2013. For two years Chan served as a Pfeiffer Postdoctoral Instructor in CAAM at Rice, and in 2015 went to work as a postdoctoral researcher in mathematics at Virginia Tech, where his mentor was Tim Warburton, formerly a member of the CAAM department at Rice. “I give Tim a lot of the credit for helping me change direction and encouraging me along the way. Tim is an incredible mentor. His thinking is very rapid-fire, and he helps you push past what you think you can do. There was a time in 2015-2016 when we were publishing a new paper every month and a half,” he said.
Chan’s father is from Hong Kong, his mother from Taiwan, and they met at Lamar University in Beaumont in Texas. He was a chemical engineer, and she majored in computer science and taught at Lamar after graduating. Chan’s father later went to work for Texaco, and the family moved to Houston when Jesse was five. “There’s a deep appeal to mathematics in the kind of work I’m doing. It’s like peeling back a bit of reality and figuring out how to change it,” he said.