In this talk, we proposes a novel two-phase magnetohydrodynamics (MHD) diffuse interface model based on the mass-conserved Allen-Cahn equation and derives its associated energy equation. By integrating the unified SAV-ZEC approach, a technique for converting an implicit integral to explicit form, and a second-order pressure projection method, we design a highly efficient and massconserving numerical scheme, transforming the complex coupled saddle point problem into several univariate elliptic type equations. This scheme first achieves complete decoupling of all variables while holding second-order accuracy in time. Then, we rigorously prove the well-posedness and unconditional energy stability of the scheme. The effectiveness of the model and the scheme are validated by simulating several benchmark problems. Numerical simulations confirm that the magnetic field suppresses the Kelvin-Helmholtz (KH) instability, and reveal a new mechanism: the suppression effect of a normal applied magnetic field is more significant than that of a tangential applied one. Furthermore, simulations of the droplet dripping process show that the applied magnetic field also inhibits droplet formation. Interestingly, the suppression effect is again more pronounced for a normally applied field.

苏海燕, 新疆大学数学与系统科学学院教授、博士生导师, 长期从事复杂不可压流体动力学问题的建模、高性能算法设计及其理论分析研究。主持国家自然科学基金面上项目 1 项, 获批 2022 年度新疆维吾尔自治区"天山英才"青年拔尖人才专项和杰出青年基金, 荣获 2023 年第十一届新疆青年科技奖。其研究工作主要聚焦复杂磁流体动力学问题的建模、高性能计算与理论分析, 开展了系统而深入的研究。在 CMAME、SIAM JSC、JSC、ESAIM: M2AN 等国际重要学术期刊发表 SCI 论文 50 余篇。相关研究成果获自治区自然科学奖一等奖、二等奖及自治区优秀论文三等奖。