Tsz Shun Eric Chung, Chinese University of Hong Kong
Room 706 ,No. 6 Science Building
In this talk, we present multi-continua upscaling methods for multiscale problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are intended for problems without scale separation and high contrast, which often occur in applications. In our method, the local solutions are used as a forward map from local averages (constraints) of the solution in oversampling region. This local fine-grid solution is further used to formulate the coarse-grid problem. Our approach is discussed on several examples and applied to flow problems in porous and fracture media. The numerical results show that we can achieve good accuracy using our new concepts for these complex problems. We will also present an extension of this method to nonlinear problems. This is a joint work with Yalchin Efendiev, Wing Tat Leung, Maria Vasilyeva, Yating Wang and Mary Wheeler.