报告题目：Dual-porosity-Stokes model and finite element method for coupling dual-porosity flow and free flow
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.
何晓明，博士，副教授，先后任美国Missouri S&T大学的Assistant Professor和Associate Professor。主持或共同主持美国国家级研究项目12项。发表和录用sci国际论文38篇，会议论文7篇，包括国际计算数学优秀期刊： Numerische Mathematik，SIAM Journal on Scientific Computing，SIAM Journal on Numerical Analysis等。同时担任多个国际数学期刊IJNAM，ANM，CMA，DCDS，JCAM，IJNAM的编委工作，是ACM,AMM，IJCM， CJAM，IJNAM ,JCP, JSC,NA,SIAM JNA,SIAM JSC等20余个国际期刊的审稿专家。