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。
