A three-level multi-continua upscaling method for flow problems in fractured porous media

TL;DR

This paper introduces a three-level multiscale upscaling method for flow in fractured porous media, combining nonlocal multi-continua and GMsFEM techniques to efficiently handle complex heterogeneities.

Contribution

It presents a novel three-level upscaling approach that integrates NLMC and GMsFEM for improved efficiency in fractured media flow simulations.

Findings

Effective reduction in computational cost.

Accurate representation of fractured media flow.

Enhanced locality in the upscaled system.

Abstract

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.