题目一：Sharp interface modeling and simulations of two-phase ferrofluid flows.
内容简介：We propose a novel sharp interface model to describe the behavior of two-phase ferrofluid flows with unmatched densities. The model couples the Navier–Stokes equations for incompressible fluid motion with an advection-reaction equation for the magnetization field, incorporating precise jump conditions at the interface. Utilizing the techniques by Barrett, Garcke, and Nurnberg (BGN), we establish a mathematical relationship between the parameterization of the interface and its mean curvature, enabling an accurate description of the interface geometry and capturing the dynamics at the sharp interface explicitly. To solve the model, we develop a fully discrete backward Euler arbitrary–Lagrangian–Eulerian (ALE) finite element method, enhanced with a specialized mesh velocity governed by a harmonic equation to maintain mesh quality throughout the simulation. Extensive numerical examples are presented to verify the validity of the proposed model, illustrate the accuracy of the numerical scheme, and simulate the benchmark “Rosensweig instability” in both two and three dimensions.
报告人：王冀鲁
报告人简介：哈尔滨工业大学（深圳）教授、博士生导师，国家高层次青年人才，此前为北京计算科学研究中心特聘研究员。王冀鲁的研究兴趣为偏微分方程数值解，包括关于浅水波方程、多孔介质中不可压混溶驱动模型、薛定谔方程以及分数阶方程的数值方法。主持国家自然科学基金面上项目和深圳市杰出青年研究项目，参与国家自然科学基金重点项目等。
题目二：High-order structure-preserving Runge-Kutta methods for the nonlinear schrodinger equation.
内容简介：A novel family of high-order structure-preserving methods is proposed for the nonlinear Schrodinger equation. The methods are developed by applying the multiple relaxation idea to the different Runge--Kutta methods. It is shown that the multiple relaxation Runge--Kutta methods can achieve high-order accuracy in time and preserve multiple original invariants at the discrete level. Several numerical experiments are carried out to support the theoretical results and illustrate the effectiveness and efficiency of the proposed methods.
报告人：李东方
报告人简介：华中科技大学数学与统计学院教授，博导，国家级青年人才。主持国家级课题6项。主要从事微分方程数值解、机器学习和信号处理等领域的研究工作。尤其在微分方程保结构算法和分数阶微分方程的高效数值算法和理论上取得一些有意义的进展。相关工作发表在《SIAM. J. Numer. Anal.》，《SIAM. J. Sci. Comput.》、《Math. Comput》、《J. Comp. Phys.》等多个国际著名计算学科SCI期刊上，多篇为高被引论文。
时 间：2025年3月25日（周二）下午18：30开始
地 点：石牌校区南海楼124会议室
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2025年3月21日