A Multiscale Method Coupling Network and Continuum Models in Porous Media

报告主题A Multiscale Method Coupling Network and Continuum Models in Porous Media


报告人Professor Richard Tsai, Department of Mathematics, University of Texas at Austin






摘要: We present a numerical multiscale method for coupling mass conservation laws at the continuum scale with a discrete, pore scale network model for two-phase flow in porous media.Our method evaluates the continuum equation by simulations using small representative networks centering at different physical locations, and thereby computes the effective dynamics of the two phase flow at the continuum scale.

      On the other hand, the initial and boundary data for the network simulations are determined by the variables used in the continuum model.

      The proposed algorithm also allows for a new coupling mechanism in which network properties such as conductivities or even the connectivity may be a function of the effective properties that take place at a much larger length scale. This particular feature enables us to incorporate a dynamic fracture model in our multiscale model. In numerical examples and by homogenization analysis we showed that the proposed multiscale coupling method indeed computes with some detailed features of the network model with a computational efficiency which is closer to that of simulations with only continuum equations.

     This is joint work with J. Chu, B. Engquist, and M. Prodanovic.


报告人简介Richard Tsai教授于1995年在国立台湾大学获数学学士学位,1999年和2002年在UCLA获数学硕士和博士学位,导师为Stanley Osher教授。他2002-2004年在普林斯顿大学高等研究院任Veblen Research Instructor2004年至今在University of Texas at Austin任职,任助理教授、副教授。Richard Tsai教授的研究兴趣广泛,包括多尺度问题及数值计算、反问题和优化问题、高频波问题以及水平集方法和应用。他至今在发表了30余篇期刊论文和10余篇会议论文,其中被MathSciNet上收录的33篇文章被合计引用423次。他还是2006Alfred P.Sloan Fellowship2007Frank Gerth III Research Fellowship2012Moncrief GRand Challenge Award的获得者。



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