  In this work, we present an upscaled model for mixed dimensional coupled flow
problem in fractured porous media. We consider both embedded and discrete
fracture models (EFM and DFM) as fine scale models which contain coupled system
of equations. For fine grid discretization, we use a conservative finite-volume
approximation. We construct an upscaled model using the non-local
multicontinuum (NLMC) method for the coupled system. The proposed upscaled
model is based on a set of simplified multiscale basis functions for the
auxiliary space and a constraint energy minimization principle for the
construction of multiscale basis functions. Using the constructed
NLMC-multiscale basis functions, we obtain an accurate coarse grid upscaled
model. We present numerical results for both fine-grid models and upscaled
coarse-grid models using our NLMC method. We consider model problems with (1)
discrete fracture fine grid model with low and high permeable fractures; (2)
embedded fine grid model for two types of geometries with differnet fracture
networks and (3) embedded fracture fine grid model with heterogeneous
permeability. The simulations using the upscaled model provide very accurate
solutions with significant reduction in the dimension of the problem.
