讲座主题：Efficient and high-order algorithms with new relaxation for two-phase incompressible flows

专家姓名：李晓丽

工作单位：山东大学

讲座时间：2024年04月20日 15:00-15:30

讲座地点：数学与信息科学学院341

主办单位：hy590海洋之神平台数学与信息科学学院

内容摘要：

In this talk we present a class of fully decoupled and high-order implicit-explicit (IMEX) schemes for the two-phase incompressible flows based on the generalized scalar auxiliary variable approach with a new relaxation for Cahn-Hilliard equation and consistent splitting method for Navier-Stokes equation. These schemes are linear, fully decoupled, unconditionally energy stable, only require solving a sequence of elliptic equations with constant coefficients at each time step, and provide a new technique to preserve the consistency between original energy and modified energy. We derive that numerical solutions of these schemes are uniformly bounded without any restriction on time step size. Furthermore, we carry out a rigorous error analysis for the first-order scheme and establish optimal global error estimates for the phase function, velocity and pressure in two and three-dimensional cases. Numerical examples are presented to validate the proposed schemes.

主讲人介绍：

李晓丽，山东大学教授，博士生导师，国家高层次青年人才入选者，山东大学杰出中青年学者。中国数学会计算数学分会常务理事。主要研究领域为相场模型高精度算法与计算流体力学。在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comp., J. Fluid Mech., Math. Mod. Meth. Appl. Sci.及J Comput. Phys.等计算数学高水平期刊上发表学术论文多篇。2019年入选“博士后创新人才支持计划”，主持国家自然科学基金面上项目、青年项目等。