A fully coupled scheme using Virtual Element Method and Finite Volume for poroelasticity

Autor: Isabelle Faille, Julien Coulet, Nicolas Guy, Frédéric Nataf, Vivette Girault
Přispěvatelé: IFP Energies nouvelles (IFPEN), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Algorithms and parallel tools for integrated numerical simulations (ALPINES), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Volumes finis
Mechanical equilibrium
Discretization
Computer science
Geomechanics
Context (language use)
010103 numerical & computational mathematics
01 natural sciences
Finite volume methods
law.invention
Géomécanique
law
Fluid dynamics
Applied mathematics
Poroélasticité
0101 mathematics
Computers in Earth Sciences
[SDU.STU.AG]Sciences of the Universe [physics]/Earth Sciences/Applied geology
MSC : 65N30
74F10
76S05
Hydrogeology
Finite volume method
Poroelasticity
[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Finite element method
Computer Science Applications
Computational Mathematics
Reservoir simulation
Virtual element methods
Computational Theory and Mathematics
Polyhedral grids
Méthode des éléments virtuels
Maillages polyédriques
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Zdroj: Computational Geosciences
Computational Geosciences, Springer Verlag, 2020, 24 (2), pp.381-403. ⟨10.1007/s10596-019-09831-w⟩
ISSN: 1420-0597
1573-1499
DOI: 10.1007/s10596-019-09831-w⟩
Popis: International audience; In this paper, we design and study a fully coupled numerical scheme for the poroelasticity problem modelled through Biot’s equations. The classical way to numerically solve this system is to use a finite element method for the mechanical equilibrium equation and a finite volume method for the fluid mass conservation equation. However, to capture specific properties of underground media such as heterogeneities, discontinuities and faults, meshing procedures commonly lead to badly shaped cells for finite element based modelling. Consequently, we investigate the use of the recent virtual element method which appears as a potential discretization method for the mechanical part and could therefore allow the use of a unique mesh for the both mechanical and fluid flow modelling. Starting from a first insight into virtual element method applied to the elastic problem in the context of geomechanical simulations, we apply in addition a finite volume method to take care of the fluidconservation equation. We focus on the first order virtual element method and the two point flux approximation for the finite volume part. A mathematical analysis of this original coupled scheme is provided, including existence and uniqueness results and a priori estimates. The method is then illustrated by some computations on two or three dimensional grids inspired by realistic application cases.
Databáze: OpenAIRE
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