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数学学院、所2021年系列学术活动(第208场):王素林 助理教授 湖南大学

发表于: 2021-12-09   点击: 

报告题目:Total Variation Bounded Flux Limiters For High Order Finite Difference Schemes Solving Scalar Conservation Laws

报 告 人:王素林 助理教授 湖南大学

报告时间:2021年12月16日 上午10:00-11:00

报告地点:腾讯会议 ID:921-222-117 会议链接:https://meeting.tencent.com/dm/ACS7wjIjSSjh

校内联系人:陶詹晶 zjtao@jlu.edu.cn


报告摘要:In this talk, we develop a new criterion for designing locally conservative high order finite difference methods with provable total variation stability for solving one-dimensional scalar conservation laws by measuring the total variation of an expanded vector. This expanded vector is created from grid values at $t^{n+1}$ and $t^n$ with ordering determined by upwinding information. Achievable local bounds for grid values at $t^{n+1}$ are obtained to provide a sufficient condition for the total variation of the expanded vector no greater than total variation of the initial. We apply the Flux-Corrected Transport type of bound preserving flux limiters to ensure that numerical values at $t^{n+1}$ are within these local bounds. When compared with traditional total variation bounded high order methods, the new method is explicitly designed and does not depend on mesh-related parameters. Numerical results are produced to demonstrate: the total variation of the numerical solution is always bounded by that of the initial; the order of accuracy is not sacrificed. When the total variation bounded flux limiting method is applied to a third order finite difference scheme, we show that the third order of accuracy is maintained from the local truncation error point of view.


报告人简介:王素林,湖南大学数学学院,助理教授。2012年6月于中国地质大学(武汉)获得理学学士学位;2019年5月于美国 Michigan Technological University 获理学博士学位,师从徐正富教授。2019年8月至2021年7月,在美国 Michigan State University 做博士后,指导老师为 Keith Promislow 和 Andrew Christlieb;2021年9月至今,在湖南大学数学学院信息与计算科学系任助理教授。主要从事和研究兴趣为若干类偏微分方程(组)的科学计算和理论分析、医学图像的降噪(数值优化)等方面的研究。