Multiscale Finite Volume Method for Discrete Fracture Modeling on Unstructured Grids

The presentation will address the recently developed multiscale method for Discrete Fracture Modeling (DFM) on unstructured grids. The fine-scale discrete system is obtained by imposing tetrahedron (triangular for 2D domains) grid cells, while lower-dimensional fractures are imposed at the grid interfaces. The DFM approach is then used to describe the transmissibility coefficients for all the interfaces, including those with the lower-dimensional fractures. On this fine-scale discrete system, a new algebraic multiscale formulation is developed, which first imposes two sets of coarse- and dual-coarse grids. The former grid is essential for conservative multiscale formulations, while the second one is used for the calculation of local multiscale basis functions. The coarse-scale partitioning of the fracture and matrix domains is flexible and totally independent. Moreover, the multiscale basis functions are constructed for both the matrix and fracture domains. The performance of the developed multiscale method is systematically assessed for 2D and 3D test cases. It is shown that the method (with no multiscale iterations) provides accurate results, even for complex fractured systems. The extension to an iterative Multiscale strategy is then illustrated to prove the capability of convergence to the fine scale reference. As such, the presented multiscale method proves a promising framework for real-field application of DFM models.

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