报告题目：Efficient fully-discrete finite element scheme for the ferrohydrodynamic Rosensweig model and simulations of ferrofluid rotational flow problems

报告人：张国栋

报告时间：2024年10月19日（周六）上午12:00开始

报告地点：数学楼315会议室

报告摘要：This talk focuses on numerical approximations of the ferrohydrodynamic (FHD) Rosensweig model of ferrofluids, which comprises the Navier-Stokes equations, the angular momentum equations, the magnetization equations, and the magnetostatic equation, as well as the simulations of the ferrofluid rotational flow problems. The model's strong coupling feature, encompassing both linear and nonlinear aspects, poses a significant challenge in the development of efficient numerical algorithms. By introducing a new nonlocal auxiliary variable and constructing an ordinary differential equation with a special structure for it, we can simplify the complex coupling terms in the modified but equivalent governing system via explicit discretization. This novel method, along with ZEC(zero energy contribution)-decoupling method, reconstruction of magnetostatic equation, and the second-order projection method for hydrodynamics, allow us to obtain a fully discrete scheme that is unconditionally energy stable, fully decoupled, linear, and second-order accurate in time. Only a few independent linear elliptic problems with constant coefficients need to be solved at each time step. In addition, simulations, including 2D/3D spin-up and annular flows, are implemented to verify the stability and accuracy of the scheme, with the numerical results exhibiting good agreement with experimental and physical analyses.

报告人简介：张国栋，博士毕业于西安交通大学，在宾夕法尼亚州立大学博士联合培养，现任烟台大学校聘教授。研究兴趣是多物理耦合问题的建模与计算，在磁流体模型解耦算法，相场模型算法分析和铁磁流体模型高效算法取得了一些较好的成果，主持结题一项国家自然科学基金青年项目，主持在研一项国家自然科学基金面上项目、一项山东省优秀青年基金项目，在SISC, M3AS, JCP期刊发表论文多篇。