Constraint Energy Minimizing Generalized Multiscale Finite Element Method for dual continuum model
For researchers in subsurface modeling, this method addresses the challenge of high heterogeneity and contrast by providing a reduced-order approach with localized basis functions.
The paper develops a novel multiscale finite element method for the dual continuum model in subsurface applications, achieving localization of basis functions and convergence dependent only on coarse mesh size, with numerical tests demonstrating performance.
The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and high contrast coefficients. To numerically compute the solutions, some types of reduced order methods are necessary. We will develop and analyze a novel multiscale method based on the recent advances in multiscale finite element methods. Our method will compute multiple local multiscale basis functions per coarse region. The idea is based on some local spectral problems, which are important to identify high contrast channels, and an energy minimization principle. Using these concepts, we show that the basis functions are localized, even in the presence of high contrast long channels and fractures. In addition, we show that the convergence of the method depends only on the coarse mesh size. Finally, we present several numerical tests to show the performance.