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，湖南大学澳门永利官网总站入口老网址，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，在湖南大学澳门永利官网总站入口老网址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。