A three-level multi-continua upscaling method for flow problems in fractured porous media
For researchers simulating flow in fractured porous media, this method reduces computational cost while maintaining accuracy, addressing a known bottleneck in multiscale modeling.
This paper proposes a three-level upscaling method for flow in fractured porous media that reduces offline computational cost compared to traditional two-level methods, achieving accurate solutions with a reduced model. Simulation results for a 2D problem with many fractures demonstrate the method's effectiveness.
Traditional two level upscaling techniques suffer from a high offline cost when the coarse grid size is much larger than the fine grid size. Thus, multilevel methods are desirable for problems with complex heterogeneities and high contrast. In this 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 system involving fractured porous media. In the next step, based on the fine grid model, we construct a nonlocal multi-continua upscaling (NLMC) method using an intermediate grid. The system resulting from NLMC gives solutions that have physical meaning. In order to enhance locality, the grid size of the intermediate grid needs to be relatively small, and this motivates using such an intermediate grid. However, the resulting NLMC upscaled system has a relatively large dimension. This motivates a further step of 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 reduced model. We present simulation results for a two-dimensional model problem with a large number of fractures using the proposed three-level method.