报告人：何晓明（Missouri University of Science and Technology）

(一)报告题目：Dual-porosity-Stokes model and finite element method for coupling dual-porosity flow and free flow

报告摘要：We propose and numerically solve a new model considering confined flow in dual-porosity media coupled with free flow in embedded macro-fractures and conduits. Such situation arises, for example, for fluid flows in hydraulic fractured tight/shale oil/gas reservoirs. The flow in dual-porosity media, which consists of both matrix and micro-fractures, is described by a dual-porosity model.  And the flow in the macro-fractures and conduits is governed by the Stokes equation. Then the two models are coupled through four physically valid interface conditions on the interface between dual-porosity media and macro-fractures/conduits, which play a key role in a physically faithful simulation with high accuracy.  All the four interface conditions are constructed based on fundamental properties of the traditional dual-porosity model and the well-known Stokes-Darcy model. The weak formulation is derived for the proposed model and the well-posedness of the model is analyzed. A finite element semi-discretization in space is presented based on the weak formulation and four different schemes are then utilized for the full discretization. The convergence of the full discretization with backward Euler scheme is analyzed. Four numerical experiments are presented to validate the proposed model and demonstrate the features of both the model and numerical method, such as the optimal convergence rate of the numerical solution, the detail flow characteristics around macro-fractures and conduits, and the applicability to the real world problems.

(二)报告题目：An introduction to the general code framework for finite element methods.

报告摘要：When students in computational mathematics start their research work, they usually encounter a critical issue: How to write a good code which is easy to be understood and modified. By using the sketch of a newly designed finite element implementation course at Missouri University of Science and Technology, we will introduce a general framework and modularization to code for the finite element methods so that the code package is both conceptually clear and easy to be modified for different equations/methods. With the key points highlighted in this talk, it will be easier for students self-learn the course slides and the conceptualized guided coding in the course recordings.

报告人简介：何晓明，美国密苏里科学技术大学副教授。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。何晓明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，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。主要研究有限元方法，区域分解方法等。在 SIAM J. Sci. Comput.,  J. Comput. Phys.,  Numer. Math.等国际知名期刊发表SCI 文章32篇, 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。

报告时间：（一）2018年1月12日(星期五) 下午14:00-15:00

      （二）2018年1月12日(星期五) 下午15:00-16:00

报告地点: 科技楼南楼702室