报告人：张智文副教授

报告题目：Robust Lagrangian Numerical Schemes in Computing Effective Diffusivities for Chaotic and Random Flows

主持人：杨畅

报告摘要：

We study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition, we numerically investigate the residual diffusion phenomenon in chaotic advection. Instead of solving the Fokker-Planck equation in the Eulerian formulation, we compute the motion of particles in the Lagrangian formulation, which is modeled by stochastic differential equations (SDEs). We propose effective numerical integrators based on a splitting method to solve the corresponding SDEs. We provide rigorous error analysis for the new numerical integrators using the backward error analysis (BEA) technique and show that our method outperforms standard Euler-based integrators. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several typical chaotic and stochastic flow problems of physical interests. The existence of residual diffusivity for these flow problems is also investigated. In addition, we report some results related to this project, especially when the flows are stochastic and/or time-dependent. 

报告时间：2024.08.02   8:00-12:00

报告地点：理学楼401室

报告人简介：Z. Zhang received his B.S. degree and Ph.D. degree in mathematics from Tsinghua University, Beijing, P.R. China, in 2006 and 2011, respectively. After his graduation, he was a postdoctoral scholar at California Institute of Technology from 2011 to 2015. He joined the University of Hong Kong as an Assistant Professor in 2015 and became an Associate Professor since 2021.  Dr. Zhang’s research interests are scientific computation. Research topics include uncertainty quantification (UQ), i.e. numerical methods for stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs), and numerical methods for partial differential equations (PDEs) arising from quantum chemistry, wave propagation, multiscale porous media, nonlinear filtering, data assimilation, and stochastic fluid dynamics.