The active flux (AF) method is a compact high-order finite volume method that simultaneously evolves cell averages and point values at cell interfaces. Within the method of lines framework, the existing Jacobian splitting-based point value update incorporates the upwind idea but suffers from a stagnation issue for nonlinear problems due to inaccurate estimation of the upwind direction, and also from a mesh alignment issue partially resulting from decoupled point value updates. I will talk about using flux vector splitting for the point value update, offering a natural and uniform remedy to the two issues. To improve robustness, I will also talk about bound-preserving (BP) AF methods for hyperbolic conservation laws, with applications to the compressible Euler equations and ideal magnetohydrodynamics. A shock sensor-based limiting will be discussed for suppressing oscillations.

段俊明, 香港中文大学(深圳)理工学院副研究员、博士生导师。分别于2016年和2021年获北京大学学士和博士学位, 随后2021至2023年于瑞士洛桑联邦理工学院开展博士后研究, 2023至2025年在德国维尔茨堡大学担任洪堡博士后。主要研究方向为流体力学中的数值方法, 包括双曲型偏微分方程的高精度数值方法和参数化时变问题的高效降阶建模等。研究成果发表于JCP、 SISC、 AIAA、CMAME等主要期刊。入选国家级青年人才项目(海外), 曾获德国洪堡基金会博士后项目资助和北京计算数学学会优秀青年论文一等奖等荣誉。