报告人：陈洁（西交利物浦大学）
时 间：4月9日上午10:00
地 点：腾讯会议APP（会议ID：540 598 179 无设置密码）
内容摘要:
We propose a multiscale method for solving the Darcy flow of a single-phase fluid in two-dimensional fractured porous media. We consider a discrete fracture-matrix (DFM) model that treats fractures as one-dimensional objects, and the flows in both the matrix and fractures respect the Darcy's law. A multipoint flux mixed finite element (MFMFE) method with the broken Raviart-Thomas (RT^{1/2}) element and the trapezoidal quadrature rule is employed to approximate the matrix velocity and pressure, which results in a block diagonal, symmetric and positive definite mass matrix for the matrix velocity on general quadrilateral grids; the one-dimensional RT_0 mixed finite element method with the one-dimensional trapezoidal quadrature rule is exploited to approximate the fracture velocity and pressure, which leads to a diagonal and positive definite mass matrix for the fracture velocity in each single fracture. All these features of the obtained mass matrices allow for velocity elimination. Multiscale basis functions are constructed for the two-dimensional matrix pressure following the generalized multiscale finite element method (GMsFEM) framework to capture the fine-scale information of heterogeneous fractured porous media and effectively reduce the degrees of freedom for the matrix pressure, while fine-grid basis functions are used for the one-dimensional fracture pressure in fractures. Various numerical tests with the oversampling technique for different fracture distributions are performed to show that the proposed multiscale method is effective and able to provide good approximations for the fine-grid solution.
个人简介：
陈洁副教授，博士生导师，分别于2004年和2007年在南京大学数学系获得学士和硕士学位，2011年在南洋理工大学获得博士学位；于2011/08-2012/10在香港科技大学做博士后研究，于2012/11-2013/03在沙特国王大学做博士后研究；2013/04进入西安交通大学数学与统计学院工作，2019/08进入西交利物浦大学工作。研究方向包括有限元方法，计算流体力学，油藏模拟。在Mathematics of Computation, Journal of computational physics, International Journal for Numerical Methods in Engineering等国际权威期刊上发表论文二十余篇，主持和参与面上项目、青年基金、博士后特等资助、CMG基金、JS大数据与小数据分析方法及应用等十余项科研项目。担任包括Journal of Computational Physics, Computer Methods in Applied Mechanics and Engineering, Water Resources Research, International Journal for Numerical Methods in Engineering在内20多个国际期刊的审稿人。担任教育部学位论文评审专家。2019年，陈洁参加第8届华人数学家大会并做45分钟邀请报告。
联系人：陈黄鑫
