Mathematical Sciences Department
Numerical Methods Seminar
Juntao Huang, Texas Tech University
Monday, October 9, 2023
11:00 am - 12:00 pm
Atwater Kent 219
Title: Structure-preserving moment models for the radiative transport and free surface flows
Abstract: The computational cost of solving high-dimensional mathematical models in physics and engineering often poses a significant challenge. This talk focuses on strategies for reducing model complexity while preserving essential mathematical structures, offering a pathway to more efficient and accurate numerical solutions.
In the first part, we introduce our machine learning-based approach for constructing moment models for radiative transport equations. Through carefully designed neural network architectures, we ensure the stability (or hyperbolicity) of these moment models. Additionally, we delve into other critical mathematical attributes, such as physical characteristic speeds.
In the second half of the talk, we shift our focus to the incompressible Navier-Stokes equations with free surfaces. We explore a novel class of models that describe this system, traditionally modeled using shallow water equations. We demonstrate the rotational invariance and hyperbolicity of these newly-derived shallow water moment models.
Short bio: Juntao Huang is an Assistant Professor at Texas Tech University. He obtained the Ph.D. degree in Applied Math in 2018 and the bachelor degree in 2013 from Tsinghua University. Prior to joining Texas Tech University in 2022, he worked as a visiting assistant professor at Michigan State University. His current research interests focus on the design and analysis of numerical methods for PDEs and, more recently, using machine learning to assist traditional scientific computing tasks. Topics of special interests include adaptive sparse grid discontinuous Galerkin (DG) methods, structure-preserving machine learning moment closures for kinetic models, structure-preserving time discretizations for hyperbolic equations, and boundary schemes for the lattice Boltzmann method.