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Abstract

Summary

Modelling the interactions between mechanical deformations and fluid flow in a porous media leads to the well known Biot system. This system involves two coupled equations obtained from the mechanical equilibrium and from the fluid mass conservation. The classical way to numerically solve this system is to use one discretisation method for each conservation equation, usually with a finite element method for the mechanical part and a finite volume method for the fluid part. However, the meshing of specific geometries encountered in underground medias related to heterogeneities, discontinuities or faults commonly lead to badly shaped cells not suited to finite element based modelling.

The recent development of the virtual element method, which can be seen as an extension of legacy finite element to more general meshes, makes it appear as a potential discretisation method for the mechanical part. More specifically, [ ] provided a first insight into virtual element method applied to the elastic problem in the context of geomechanical simulations. The originality of our work is to design and study a numerical scheme coupling the lowest order virtual element method applied to the mechanical conservation equation with a finite volume scheme method applied to the fluid conservation equation.

A mathematical analysis of this original coupled scheme is provided, including existence and uniqueness results and a priori estimates, for the case of a two points finite volume scheme modelling of fluid flow. The coupled scheme is illustrated by some computations on two or three dimensional grids coming from realistic cases. In the presentation, the coupling with more elaborate finite volume schemes such as multi point flux approximation schemes is also investigated.

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/content/papers/10.3997/2214-4609.201802271
2018-09-03
2024-04-24

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Fully Coupled Schemes Using Virtual Element And Finite Volume Discretisations For Biot Equations Modelling
Conference Proceedings 2018, 1 (2018); https://doi.org/10.3997/2214-4609.201802271
/content/papers/10.3997/2214-4609.201802271
/content/papers/10.3997/2214-4609.201802271
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