Multi-physics flux coupling for hydraulic fracturing modelling within INMOST platform.

*(English)*Zbl 1450.65097The author presents a collocated finite volume method for a coupled system of equations in multiple domains. Each domain is characterized by the properties of heterogeneous media and features a distinctive multi-physics model. The coupled systems of equations, corresponding to multiple unknowns, results in a vector flux. The finite volume method requires continuity of intradomain and interdomain vector fluxes. The continuous flux is derived using an extension of the harmonic averaging point concept. The collocated coupling of the equations results in a saddle-point problem which leads to inf-sup stability problems. These problems are handled thanks to the eigen-splitting of indefinite matrix coefficients involved in the flux expression. The application of the techniques implemented within INMOST (integrated numerical modelling and object-oriented supercomputing technologies) platform to hydraulic fracturing problem is shown.

Reviewer: Abdallah Bradji (Annaba)

##### MSC:

65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

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

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

##### Keywords:

multi-physics; Darcy equation; poroelasticity; hydraulic fracturing; finite volume method; inf-sup stability; harmonic averaging point##### Software:

INMOST
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\textit{K. M. Terekhov}, Russ. J. Numer. Anal. Math. Model. 35, No. 4, 223--237 (2020; Zbl 1450.65097)

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