数学与计算机科学学院

2018.1.4

摘要：The Navier-Stokes equation coupled with the Darcy equation through interface conditions has attracted scientists’ attention due to its wide range of applications and significant difficulty in the nonlinearity and interface conditions. This presentation discusses a multi-physics domain decomposition method for decoupling the coupled Navier-Stokes-Darcy system with the Beavers-Joseph interface condition. The wellposedness of this system is first showed by using a branch of singular solutions and the existing theoretical results on the Beavers-Joseph interface condition. Then Robin boundary conditions on the interface are constructed based on the physical interface conditions to decouple the Navier-Stokes and Darcy parts of the system. A parallel iterative domain decomposition method is developed according to these Robin boundary conditions and then analyzed for the convergence, especially for the realistic parameters. Numerical examples are presented to illustrate the features of this method and verify the theoretical results.

报告人简介：何晓明，美国密苏里科学技术大学副教授。 2002年毕业于四川大学数学系获学士学位，2009年在弗吉尼亚理工大学获博士学位(师从Tao Lü教授)，2009年至2010年在佛罗里达州立大学作博士后师从（Prof. Max Gunzburger）。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。任计算数学领域国际期刊International Journal of Numerical Analysis & Modeling的编委，任SIAM Central States Section第一任主席和前两届年会的组织委员会主席。其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，计算流体动力学，随机偏微分方程，非线性偏微分方程，反馈控制问题，计算电磁学等。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SIAM Journal on Scientific Computing，Journal of Computational Physics，Mathematics of Computation，Numerische Mathematik，SIAM Journal on Numerical Analysis，IEEE Transactions on Plasma Science等杂志发表论文30多篇。