报告题目一: Bound- and Positivity-preserving AWENO Schemes for the Five-equation Model of Two-component Flows

报告时间：2023年9月20日上午9:00-10:00

报告地点：龙洞行政楼610报告厅

报告人：谷亚光副教授 华南理工大学

主持人：况阳

报告摘要: 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 design quasi-conservative finite difference AWENO schemes up to the ninth order for the five-equation transport model (Allaire, 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 AWENO schemes, while preserving the equilibrium solutions simultaneously. Once the BP-P limiters are used, the numerical solutions are oscillatory due to the suddenly drastic scale transition of the density, pressure, and so on, especially near strong shock and/or rarefaction waves. To this end, we modify the classic WENO-Z weights so that the new AWENO schemes, denoted as Ai-AWENO schemes, are affine-invariant and can resolve the transition of different scales. In addition, we will systematically derive BP-P-related CFL conditions when the Lax-Friedrichs numerical flux is applied. If time permits, we also introduce a path-conservative Ai-AWENO scheme with central upwind numerical flux, i.e., PCCU- AWENO for short, for the model. A variety of one- and two-dimensional test problems illustrate the high order of accuracy, effectiveness, and robustness of the proposed schemes. 

报告人简介：谷亚光博士于2019年博士毕业于香港浸会大学，2020至2022年在中国海洋大学做博士后，2022年9月至今在华南理工大学数学学院任副教授。研究兴趣为流体力学的高精度高分辨率数值方法。

报告题目二: An inverse Lax-Wendroff procedure for finite difference schemes on the Cartesian mesh

报告时间：2023年9月20日上午9:00-10:00

报告地点：龙洞行政楼610报告厅

报告人：卢键方副教授 华南理工大学

主持人：解斌强

报告摘要: In this talk, we introduce the so-called inverse Lax-Wendroff (ILW) boundary treatment for finite difference approximations on the Cartesian mesh. As the domain boundary may intersect with the grid in arbitrary fashion, then it may require a restricted CFL condition for the sake of stability. Also, the wide stencil of the high order finite difference method also brings challenges in the boundary treatment. We consider the convection-diffusion problems and illustrate the idea of ILW numerical boundary treatment. By the ILW procedure, the evaluation on the ghost points could be stable and high order. The numerical tests are shown to demonstrate the robustness of the proposed algorithm.

报告人简介：卢键方博士于2010年在中国科学技术大学获得理学学士学位，2016年博士毕业于中国科学技术大学，2016至2018年在北京计算科学研究中心做博士后，2018年至2021年在华南师范大学华南数学应用与交叉研究中心当讲师，2021年8月至今在华南理工大学数学学院任副教授。研究兴趣包括流体力学的高精度高分辨率数值方法和非局部扩散问题的间断有限元方法。