Lecture Content：

Numerical study on compressible two-medium flows has been a hot issue in recent decades due to broad applications in gas bubble dynamics, underwater explosion, inertial confinement fusion, and so on. In this study, we present fifth-, seventh- and ninth-order finite difference quasi-conservative alternative WENO (AWENO) schemes with Lax-Friedrichs numerical flux for the five-equation transport model (Allaire, et. al., JCP, 2002) of two-medium flows with the stiffened gas equation of state. We propose a uniformly high order flux-based bound- and positivity-preserving (BP-P) limiters for the scheme, while preserving the equilibrium solutions simultaneously. Once the BP-P limiters are used, oscillations may be generated at material interface. To this end, we introduce the affine-invariant WENO interpolations, which take care of structures, especially in small scales. In addition, we will systematically derive the BP-P CFL conditions. Numerical examples demonstrate robustness and effectiveness of the proposed schemes.

Speaker Introduction:

Gu Yaguang is an Associate Professor who completed his undergraduate studies at the College of Mathematics and Information Science (now the College of Mathematical Sciences) at Hebei Normal University. He obtained his master’s degree from the Department of Mathematics at the University of Macau and his PhD from the Department of Mathematics at Hong Kong Baptist University. He conducted postdoctoral research at the College of Mathematical Sciences, Ocean University of China, and currently teaches at the School of Mathematics at South China University of Technology. His research focuses on high-precision numerical methods for hyperbolic conservation laws, and his work has been published in journals such as the Journal of Computational Physics (JCP), Journal of Scientific Computing (JSC), and Communications in Computational Physics (CiCP).