题目: Linearized supplementary variable method for the Cahn-Hilliard-Navier-Stokes system

主讲人：龚跃政 教授

时间：2026年09月04日（周五）15:00 —16:30

地点：理学院楼308

主办单位：理学院

主讲人简介:

龚跃政，南京航空航天大学数学学院教授、博导，长期致力于偏微分方程的保结构算法理论与应用研究，重点关注数值方法对数学结构和物理性质的保持机制，探索高效高精度的计算方法以解决多物理场耦合问题。主持国家级项目2项、省部级项目2项等。发表SCI论文60余篇。

摘要：

In this talk, we develop a linearized supplementary variable method (LSVM) for the Cahn-Hilliard-Navier-Stokes system to construct linear, constant-coefficient, decoupled, and unconditionally energy-stable second-order schemes. Two scalar correction parameters are introduced to eliminate the energy defect arising from the explicit treatment of nonlinear and coupling terms, so that the schemes can be implemented in a decoupled manner with constant coefficients. Each time step requires only solving independent elliptic equations, generalized Stokes problems, and a small $2\times2$ linear system, with no nonlinear iterations. We rigorously prove mass conservation, unconditional energy stability, and unique solvability of the proposed schemes. Numerical experiments verify the convergence rates, mass conservation, energy dissipation, and constant-coefficient decoupling performance. Further simulations of typical interfacial-flow problems, including droplet dynamics and Rayleigh-Taylor instability, demonstrate the effectiveness and robustness of the proposed schemes.