A fully conforming finite volume approach to two-phase flow in fractured porous media.

*(English)*Zbl 1454.65137
Klöfkorn, Robert (ed.) et al., Finite volumes for complex applications IX – methods, theoretical aspects, examples. FVCA 9, Bergen, Norway, June 15–19, 2020. In 2 volumes. Volume I and II. Cham: Springer. Springer Proc. Math. Stat. 323, 547-555 (2020).

Summary: In many natural and technical applications in porous media fluid’s flow behavior is highly affected by fractures. Many approaches employ mixed-dimensional models that model thin features as dimension-reduced manifolds. Following this idea, we consider porous media where dominant heterogeneities are geometrically represented by sharp interfaces. We model incompressible two-phase flow in porous media both in the bulk porous medium and within the fractures. We present a reliable and geometrically flexible implementation of a fully conforming finite volume approach within the DUNE framework for two and three spatial dimensions. The implementation is based on the new dune-mmesh grid implementation that manages bulk and surface triangulation simultaneously. The model and the implementation are extended to handle fracture junctions. We apply our scheme to benchmark cases with complex fracture networks to show the reliability of the approach.

For the entire collection see [Zbl 1445.65003].

For the entire collection see [Zbl 1445.65003].

##### MSC:

65N08 | Finite volume methods for boundary value problems involving PDEs |

65M22 | Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs |

76S05 | Flows in porous media; filtration; seepage |

76T06 | Liquid-liquid two component flows |

76M12 | Finite volume methods applied to problems in fluid mechanics |

74S10 | Finite volume methods applied to problems in solid mechanics |

35Q35 | PDEs in connection with fluid mechanics |

35Q74 | PDEs in connection with mechanics of deformable solids |

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\textit{S. Burbulla} and \textit{C. Rohde}, Springer Proc. Math. Stat. 323, 547--555 (2020; Zbl 1454.65137)

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##### References:

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