Characteristic-featured troubled-cell indicator for Conservation Laws based on Artificial Neural Network
Speaker
Prof. Tie-Gang Liu
Beihang University
Abstract

We use exact solutions of one-dimensional Burgers equation to train an artificial neuron as a shock wave detector. The expression of the artificial neuron detector is then modified into a practical form to reflect admissible jump of eigenvalues. We show the working mechanism of the practical form is consistent with compressing or intersecting of characteristic curves. In addition, we prove there is indeed a discontinuity inside the cell detected by the practical form, and smooth extrema and large gradient regions are never marked. As a result, we apply the practical form to numerical schemes as a shock wave indicator with its easy extension to multi-dimensional conservation laws. Numerical results are present to demonstrate the robustness of the present indicator under Runge-Kutta Discontinuous Galerkin framework, its performance is generally compared to TVB-based indicators more efficiently and accurately. 

About the Speaker

刘铁钢,北京航空航天大学研究生院副院长兼培养处处长,数学科学学院教授、博士生导师。分别于1986年和1989年获得北京大学数学系理学学士和硕士。2001年获新加坡国立大学机械工程系计算流体力学工学博士。1989--1995年,在中国科学院计算数学研究所工作。1999--2007年,在新加坡科技局高性能计算研究所工作。2007年8月回国任教。主要研究方向为可压缩多介质流体数值方法、气动优化与设计、空化流建模及数值模拟、爆炸冲击中流-固耦合及动边界问题数值模拟等。主持和参与国家自然科学基金重大计划集成、国家自然科学基金重点、国际合作重点、科技部重点项目。

学术兼职:

曾任教育部高等教育数学专业类教学指导委员会秘书长、中国数学会理事、中国工业与应用数学学会常务理事、中国计算数学学会常务理事、北京数学学会常务理事。现任北京计算数学学会常务理事,《数值计算与计算机应用》《计算物理》等国内期刊及《Numerical MathematicsTheoryMethods and Applications》、《Advances in Applied Mathematics & Mechanics》国际SCI期刊编委。


Date&Time
2021-11-09 10:00 AM
Location
Room: Tencent Meeting
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