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Dual-porosity-Stokes model and finite element method for coupling dual-porosity flow and free flow
发布时间: 2017-12-18     16:12   【返回上一页】 发布人:Xiaoming He & 杨霄锋


北京师范大学数学科学学院

 

                             计算数学学术报告

报告一:
 

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

报告人:Xiaoming He Missouri University of Science and Technology

时间地点: 2017122210:00- 10:40 后主楼1223

邀请人:曹外香

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.

报告二:
 

报告题目:Some advances on the algorithms development for the two-phase model for the EWOD with moving contact lines

 

报告人:杨霄锋University of South Carolina

时间: 20171222 10:40- 11:20 后主楼1223

邀请人:张辉

报告摘要: Electrowetting-on-dielectric (EWOD) is a versatile tool in microfluidics/liquid lens because it enables control over fluid drop shape and flow by electrical signals alone. We consider the numerical approximations of the phase-field EWOD model that incorporates the variable densities, viscosities, moving contact line boundary conditions, electric displacement and charge densities. The model is a highly nonlinear, coupled system that consists of incompressible Navier-Stokes equations with the generalized Navier boundary condition, the Cahn-Hilliard equation in the conserved form, and the Maxwell equations. For some simplified case, we made some advances in developing efficient, unconditionally energy stable numerical schemes, in particular, linear and decoupled schemes. Some further discussions are aslo presented.