Stony Brook University Applied Mathematics and Statistics

Speaker: Xiaolin Li
Location: B205
Date and Time: March 21 (Fri), 12:00 PM - 1:00 PM KST

About the Speaker: Dr. Xiaolin Li

• Professor, Dept. of Applied Mathematics and Statistics | Stony Brook University
• Assistant Professor, Dept. of Mathematics and Dept. of Computer Science | Indiana University-Purdue University at Indianapolis
• Assistant Professor, Department of Mathematics | New Jersey Institute of Technology
• Associate Research Scientist | Courant Institute of Mathematical Sciences
• Ph.D. in Applied Mathematics | Columbia University
• M.S. in Applied Mathematics | Columbia University
• B.S. in Physics | Wuhan University

Abstract
Nonlinear hyperbolic PDEs, due to the intersection of characteristics, lead to either multivalued solutions or discontinuities. In physics, only the latter is acceptable. These discontinuities fall under the category of "weak solutions," which satisfy the integral form of the PDE rather than the pointwise form.

The front tracking method is specifically designed to handle such discontinuities within finite difference and finite element schemes for numerically solving PDEs. In two and three dimensions, the challenge extends beyond coupling the interior solution with the discontinuity—we must also manage topological bifurcations. In this talk, we will discuss the implementation of this method and its applications to physical phenomena such as fluid interface instabilities, jet mixing, and deposition and erosion.