A fully coupled scheme using virtual element method and finite volume for poroelasticity

Coulet, Julien; Faille, I.; Girault, Vivette; Guy, Nicolas; Nataf, Frédéric

doi:10.1007/s10596-019-09831-w

Cited by 28 publications

(22 citation statements)

References 30 publications

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“…We use this hybrid framework in the current work due to its availability. However, recent works have shown the current modelling framework to be suitable for subsurface applications where complex geometrical structures can lead to irregular grids not easily handled by standard finite‐element methods 56,58 …”

Section: Numerical Frameworkmentioning

confidence: 99%

Anisotropic dual‐continuum representations for multiscale poroelastic materials: Development and numerical modelling

Ashworth

Doster

2020

Num Anal Meth Geomechanics

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Summary Dual‐continuum (DC) models can be tractable alternatives to explicit approaches for the numerical modelling of multiscale materials with multiphysics behaviours. This work concerns the conceptual and numerical modelling of poroelastically coupled dual‐scale materials such as naturally fractured rock. Apart from a few exceptions, previous poroelastic DC models have assumed isotropy of the constituents and the dual‐material. Additionally, it is common to assume that only one continuum has intrinsic stiffness properties. Finally, little has been done into validating whether the DC paradigm can capture the global poroelastic behaviours of explicit numerical representations at the DC modelling scale. We address the aforementioned knowledge gaps in two steps. First, we utilise a homogenisation approach based on Levin's theorem to develop a previously derived anisotropic poroelastic constitutive model. Our development incorporates anisotropic intrinsic stiffness properties of both continua. This addition is in analogy to anisotropic fractured rock masses with stiff fractures. Second, we perform numerical modelling to test the DC model against fine‐scale explicit equivalents. In doing, we present our hybrid numerical framework, as well as the conditions required for interpretation of the numerical results. The tests themselves progress from materials with isotropic to anisotropic mechanical and flow properties. The fine‐scale simulations show that anisotropy can have noticeable effects on deformation and flow behaviour. However, our numerical experiments show that the DC approach can capture the global poroelastic behaviours of both isotropic and anisotropic fine‐scale representations.

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Section: Numerical Frameworkmentioning

confidence: 99%

Anisotropic dual‐continuum representations for multiscale poroelastic materials: Development and numerical modelling

Ashworth

Doster

2020

Num Anal Meth Geomechanics

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“…Two or multi-point flux approximation based techniques are described in [21,22] and gradient schemes in [10]. Virtual Element (VEM) based discretizations have also been recently investigated to ease the mesh generation process in complex DFMs, as in [23] where the VEM is coupled to the Boundary Element method, and in [24], in [25] for poro-elasticity problems, or in [26] where an arbitrary order mixed VEM formulation is proposed.…”

Section: Introductionmentioning

confidence: 99%

An optimization approach for flow simulations in poro-fractured media with complex geometries

2021

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A new discretization approach is presented for the simulation of flow in complex poro-fractured media described by means of the Discrete Fracture and Matrix Model. The method is based on the numerical optimization of a properly defined cost-functional and allows to solve the problem without any constraint on mesh generation, thus overcoming one of the main complexities related to efficient and effective simulations in realistic DFMs.

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“…The computability of the projectors and of the resulting discrete operators by means of the chosen set of degrees of freedom is one of the key aspects of the method. The usability of the method in the context of the simulation of underground phenomena appeared evident since its earliest appearance, for the description of the flow in poro-fractured domains [ (Benedetto, et al 2014), (Andersen, Nilsen and Raynaud 2017), (A. Fumagalli 2018), (Coulet, et al 2020), (Mazzia, et al 2020), (Borio, Fumagalli and Scialò 2020)]. The robustness of the VEM to highly distorted and elongated elements [ (Mascotto 2018), (Berrone and and Borio 2017)] allows for an easy meshing process also in presence of multiple intersecting interfaces, without requiring modifications of the geometry of the domain.…”

Section: Introductionmentioning

confidence: 99%

The Mixed Virtual Element Method for Grids with Curved Interfaces in Single-Phase Flow Problems

Dassi

Fumagalli

Losapio

et al. 2021

SPE Reservoir Simulation Conference

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In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the physical boundary, are often met in real applications. However, they are often approximated leading to a geometrical error that might become dominant and deteriorate the quality of the results. Underground problems often involve the motion of fluids where the fundamental governing equation is the Darcy law. High quality velocity fields are of paramount importance for the successful subsequent coupling with other physical phenomena such as transport. The virtual element method, as solution scheme, is known to be applicable in problems whose discretizations requires cells of general shape, and the mixed formulation is here preferred to obtain accurate velocity fields. To overcome the issues associated to the complex geometries and, at the same time, retaining the quality of the solutions, we present here the virtual element method to solve the Darcy problem, in mixed form, in presence of curved interfaces in two and three dimensions. The numerical scheme is presented in detail explaining the discrete setting with a focus on the treatment of curved interfaces. Examples, inspired from industrial applications, are presented showing the validity of the proposed approach.

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A fully coupled scheme using virtual element method and finite volume for poroelasticity

Cited by 28 publications

References 30 publications

Anisotropic dual‐continuum representations for multiscale poroelastic materials: Development and numerical modelling

Anisotropic dual‐continuum representations for multiscale poroelastic materials: Development and numerical modelling

An optimization approach for flow simulations in poro-fractured media with complex geometries

The Mixed Virtual Element Method for Grids with Curved Interfaces in Single-Phase Flow Problems

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