Abstract
In this talk, I will introduce the generalized multiscale finite element method (GMsFEM) for single phase compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to construct permeability dependent offline basis for fast coarse-grid simulation. The offline coarse space is efficiently constructed only once based on the initial permeability field with parallel computing. A rigorous convergence analysis is performed for two types of snapshot spaces.
The analysis indicates that the convergence rates of the proposed multiscale method depend on the coarse-grid mesh size and the eigenvalue decay of the local spectral problem. To further increase the accuracy of multiscale method, residual driven online multiscale basis is added to the offline space. The construction of the online multiscale basis is based on a carefully designed error indicator motivated by the analysis. We find that online basis is particularly important for the singular source.
Rich numerical tests on typical 3D highly heterogeneous media are presented to demonstrate the impressive computational advantages of the proposed multiscale method.
Short bio
Dr. Shubin Fu is now a Van Vleck visiting assistant professor at the University of Wisconsin-Madison. He received his BS degree from Sichuan University and completed his PhD at Texas A&M University. His research interests include uncertainty quantity, data assimilation and multiscale model reduction especially its applications in science and engineering. He has published about 25 research papers in journals like Multiscale Modeling & Simulation, Journal of Computational Physics, Geophysical Journal International and Water Resources Research.
