演讲人Speaker：毛士鹏  

题目Title: A Gauss’s law preserving, helicity, mass, charge current, energy-conserving finite element method for  incompressible MHD systems

时间Date： 2025年6月12日       Time：15:00-16:00

地点Venue： H 栋 303 室

内容摘要Abstract： 

We propose a novel structure-preserving finite element scheme for the three-dimensional incompressible magnetohydrodynamic (MHD) equations. The contribution of our research is three-fold.  Firstly, the proposed scheme exactly preserves critical physical properties, including mass conservation, the magnetic Gauss’s law, charge conservation, energy conservation and magnetic/fluid helicity conservation in their respective physical limits. To the best of our knowledge, this is the first numerical method that preserves all these properties simultaneously. Secondly, it introduces the first linear scheme that upholds the helicity preserving property for MHD, thus eliminating the necessity for fixed-point iterations as seen in existing literature. Last but not least, for the resulting large linear systems, we develop efficient block preconditioners that remain robust at high fluid and magnetic Reynolds numbers by incorporating techniques such as the augmented Lagrangian method and mass augmentation. Finally, a series of numerical experiments demonstrate that our method is accurate, stable, robust under extreme physical parameters and capable of preserving all the stated physical properties, including benchmark problems of Orszag Tang vortex and driven magnetic reconnection with fluid and magnetic Reynolds numbers up to 10^6. 

个人简介(About the speaker):

毛士鹏，中科院数学与系统科学研究院研究员、博士生导师，中科院大学岗位教授。2008年博士毕业于中科院数学与系统科学研究院，2008-2012先后在在法国国家信息自动化研究院（INRIA）以及在瑞士苏黎世高工(ETH Zurich)做博士后和研究助理，2008-2019在中科院数学与系统科学研究院分别任助理研究员和副研究员，2019年4月升任研究员。主要研究兴趣为有限元方法及其应用，计算流体力学和磁流体力学，多物理场计算等。在计算数学专业刊物上发表和接受SCI论文90余篇，承担来自科技部，基金委，中物院，九所，中科院大气所等单位的重要科研任务课题10余项。