Abstract: Hydrodynamical evolution in a gravitational field arises in many astrophysical and atmospheric problems. In this presentation, we will talk about arbitrary order structure preserving discontinuous Galerkin finite element methods for the Euler equations under gravitational fields, which can exactly capture the non-trivial steady state solutions, and at the same time maintain the non-negativity of some physical quantities. In addition, we consider the Euler–Poisson equations in spherical symmetry with an equilibrium state governed by the Lane–Emden equation, and design well-balanced and total-energy-conserving discontinuous Galerkin methods. High order semi-implicit, well-balanced asymptotic preserving finite difference scheme, for all Mach Euler equations with gravitation, may also be discussed. Extensive numerical examples, including a toy model of stellar core-collapse with a phenomenological equation of state that results in core-bounce and shock formation, are provided to verify the well-balanced property, positivity-preserving property, high-order accuracy, total energy conservation, and good resolution for both smooth and discontinuous solutions.
Speaker’s Bio: Yulong Xing is a professor in the Department of Mathematics at the Ohio State University (OSU). He received his bachelor's degree from the University of Science and Technology of China in 2002, and Ph.D. in Mathematics from Brown University in 2006 under the supervision of Prof. Chi-Wang Shu. Prior to joining OSU, he worked as a Postdoctoral Researcher at Courant Institute, New York University; a staff scientist at Oak Ridge National Laboratory; a joint assistant professor at the University of Tennessee Knoxville; and an assistant professor at the University of California-Riverside. He works in the area of numerical analysis and scientific computing, wave propagation, and computational fluid dynamics.
Last Updated: October 21, 2022 - 9:42 am