报告题目：The Non-iterative Multi-physics Domain Decomposition Method for Coupled Free Flow and Porous Media Flow Problem

主 讲 人：何 晓 明

单 位：美国密苏里科学技术大学

时 间：12月9日9:00

ZOOM ID：210 089 8623

密 码：123456

摘 要：

The Stokes-Darcy and Navier-Stokes-Darcy model have attracted significant attention in the past ten years since they arise in many applications involving with coupled free flow and porous media flow such as surface water flows, groundwater flows in karst aquifers, petroleum extraction and industrial filtration. They have higher fidelity than either the Darcy or Navier-Stokes systems on their own, but coupling the two constituent models leads to a very complex system. Based on a short review about the traditional iterative domain decomposition methods for the Stokes-Darcy model, this summary presentation discusses a series of works in the past ten years for the non-iterative multi-physics domain decomposition method to solve non-stationary Navier-Stokes-Darcy (or Stokes-Darcy) model, including both the algorithm development, validation, and analysis. One key idea is to decouple the free and porous media flow through Robin type boundary conditions which arise from the three interface conditions. Another key idea is to use the lagged results from the previous time iteration step to predict the auxiliary functions needed on the interface for the domain decomposition at the current time iteration step. Optimal convergence is proved for the k-step (1≤k≤5) back backward differentiation scheme with finite element spatial discretization. Computational results are presented to illustrate the features of the proposed method.

简 介：

何晓明，美国密苏里科学技术大学副教授。主要的研究领域是计算科学与工程。研究问题主要包括界面问题，计算流体力学，计算电磁学，非线性偏微分方程，随机偏微分方程，控制问题等。他将计算数学与实际工程应用问题结合起来，在科学计算和应用领域做了大量的工作, 在国内外学术期刊发表学术论文60余篇。2002年和2005年在四川大学数学学院获学士学位和硕士学位，2009年在弗吉尼亚理工大学数学系获博士学位，2009年至2010年在佛罗里达州立大学作博士后。2010年至2016年在美国密苏里科学技术大学任助理教授，2016年晋升为副教授，并获终身教职。担任计算数学领域国际期刊International Journal of Numerical Analysis & Modeling的编委，是多个著名国际学术期刊特刊的Guest editor。2014-2016年担任SIAM Central States Section第一任主席和前两届年会的组织委员会主席。2019年起担任Midwest Numerical Analysis Day的执行委员会委员。