报告题目：Linear decoupled structure-preserving incremental viscosity splitting methods for the Cahn-Hilliard-Navier-Stokes system
报告人：付红斐 教授 中国海洋大学
摘 要：We propose first- and second-order time discretization schemes for the coupled Cahn-Hilliard-Navier-Stokes model, leveraging the incremental viscosity splitting (IVS) method. The schemes combine the scalar auxiliary variable method and the zero-energy-contribution approach, resulting in a linear, decoupled numerical framework. At each time step, they only require to solve a sequence of constant-coefficient equations, along with a linear equation with one unknown, making the algorithms computationally efficient and easy to implement. In addition, the proposed schemes are proven to be uniquely solvable, mass-conserving, and unconditional energy dissipation. Most importantly, leveraging the mathematical induction method and the regularity properties of the Stokes equation, we perform a rigorous error analysis for the first-order scheme in multiple space dimensions, establishing an unconditional and optimal convergence rate for all relevant variables under different norms. A user-defined, time-dependent parameter plays an important role in the error analysis of the proposed structure-preserving IVS methods. Ample numerical examples are carried out to verify the theoretical findings and to demonstrate the accuracy, effectiveness and efficiency of the proposed schemes. This is a joint work with my Ph. D student Baolin Kuang (况宝琳) and Prof. Xiaoli Li (李晓丽).
报告人简介：付红斐，中国海洋大学乐竞体育-中国一站式服务官网教授、博士生导师，中国工业与应用数学学会油水资源数值方法专委会委员、中国仿真学会仿真算法专业委员会委员、山东数学会理事、山东数学会计算数学专委会委员、美国数学会《数学评论》评论员，山东大学计算数学博士，美国南卡罗莱纳大学访问学者。主要从事偏微分方程数值解法、最优控制问题数值算法、分数阶微分方程数值理论和快速算法，以及计算流体力学、油藏数值模拟、相场模型等的高阶保结构算法的设计与分析等工作。近年来先后主持、参与10余项国家自然科学基金（重点、面上、青年、天元）、山东省自然科学基金（面上、青年）和中央高校基本科研业务费等，在CMAME、JCP、M2AN、JSC、ANM、ACM等计算数学顶尖和权威期刊发表SCI论文80余篇，并两次获山东省科学技术奖自然科学二等奖。
报告时间：2025年11月17日，15:30--18:00
报告地点：乐竞体育-中国一站式服务官网512
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乐竞体育-中国一站式服务官网
2025年11月14日
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