A Three-Level Multi-Continua Upscaling Method for Flow Problems in Fractured Porous Media (Communications in Computational Physics, 2019)
Traditional two level upscaling techniques suffer from a high offline costwhen the coarse grid size is much larger than the fine grid size one. Thus, multilevelmethods are desirable for problems with complex heterogeneities and high contrast. Inthis paper, we propose a novel three-level upscaling method for flow problems in fractured porous media. Our method starts with a fine grid discretization for the systeminvolving fractured porous media. In the next step, based on the fine grid model, weconstruct a nonlocal multi-continua upscaling (NLMC) method using an intermediategrid. The system resulting from NLMC gives solutions that have physical meaning. Inorder to enhance locality, the grid size of the intermediate grid needs to be relativelysmall, and this motivates using such an intermediate grid. However, the resultingNLMC upscaled system has a relatively large dimension. This motivates a further stepof dimension reduction. In particular, we will apply the idea of the Generalized Multiscale Finite Element Method (GMsFEM) to the NLMC system to obtain a final reducedmodel. We present simulation results for a two-dimensional model problem with alarge number of fractures using the proposed three-level method.
Keywords: Multiscale method; three-level scheme; multicontinuum; upscaling; GMsFEM; NLMC; fractured porous media.