The following approaches are being used for modeling fractured porous media with multiscale and multiphysics:

1)projection-based embedded discrete fracture model (pEDFM) with cell-centered finite volumes. Check DOI:10.3390/en16020928 and DOI:10.48550/arXiv.2302.10986

2) A combined eXtended Finite Element Method (XFEM) and Embedded Discrete Fracture Method (EDFM). Check DOI:10.1016/j.geoen.2023.211984 and DOI:10.1016/j.jclepro.2023.137630 and DOI:10.1002/essoar.10509306.1

3)Mixed Multiscale Finite Element Method. Check DOI:10.1029/2020WR028877 and DOI:10.1016/j.jcp.2023.112134

4)TOUGH-FLAC simulator. It links TOUGH2, an integral finite difference multiphase flow and heat transport simulator, and FLAC3D, a finite-difference geomechanical code. Check DOI:10.1016/j.compgeo.2022.105161 and DOI:10.1016/j.ijrmms.2021.104872

For a comparison of different approaches check: DOI:10.48550/arXiv.2302.10986

Which one do you prefer and why?

is there any other approach?

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