走向现代数学学术报告 - 王坤副教授（No. 727） 

题目：Second-order unconditionally maximum bound principle preserving scheme for the convective Allen-Cahn equation 

报告人：王坤 副教授（重庆大学） 

时间：2024年7月5日 15：30 

地点：东海岸校区-D实209 

摘要：Convective Allen-Cahn equation is a generalized form of the Allen-Cahn equation with the extra convective term related to a solenoidal velocity field, which inherits the maximum bound principle (MBP). By using a stabilized technique to reduce the time step constraint and defining a new auxiliary variable to reformulate the action of the velocity on the phase field, we firstly convert the convective Allen-Cahn equation into the Fokker-Planck form based on the Slotboom transforma tion. Then, adopting a quasi-symmetric finite difference method in space and an implicit-explicit (IMEX) scheme in time, we propose a new fully discrete scheme for the reformulated equations, which is proved to be unconditionally MBP preserving and have second-order accuracy in space. Moreover, to deal with the harmonicity loss and the increment of the computational cost due to the reformulation of the velocity with the auxiliary variable, we further improve the proposed scheme by reconstructing a new discrete gradient operator and deducing an efficient implementation, respectively. Finally, some numerical examples in two and three dimensions are carried out to verify the theoretical analysis and demonstrate the e ciency of the new scheme. 

个人简介：王坤，重庆大学数学与统计学院副教授、硕士生导师。毕业于西安交通大学，获理学博士学位，并曾在加拿大Alberta大学从事博士后研究。主要从事偏微分方程数值解方面的研究，包括复杂流体力学方程、趋化模型的数值分析与模拟等，其结果曾在SIAM Journal of Numerical Analysis, Journal of Computational Physics，Computer Methods in Applied Mechanics and Engineering，Communications in Computational Physics等杂志上发表。