Numerical Solution of Plate Poroelasticity Problems

Iliev, Oleg; Kolesov, Aleksandr E.; Vabishchevich, Petr N.

doi:10.1007/s11242-016-0726-7

Cited by 7 publications

(2 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Biot's model describes the coupled processes of deformation of the elastic medium and the flow of fluid. The model is macroscopic in the sense that the space containing the poroelastic medium is filled with a two-phase medium, with one phase corresponding directly to the porous medium, and the second to the fluid contained in the pores [34,24].…”

Section: Introductionmentioning

confidence: 99%

A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media

Tyrylgin¹,

Vasilyeva²,

Alikhanov³

et al. 2022

Preprint

View full text Add to dashboard Cite

In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of equations for pressures in each continuum and elasticity equations for displacements of the medium. We assume that the temporal dynamics is governed by fractional derivatives following some works in the literature. We derive an implicit finite difference approximation for time discretization based on the Caputo's time fractional derivative. A Discrete Fracture Model (DFM) is used to model fluid flow through fractures and treat the complex network of fractures. We assume different fractional powers in fractures and matrix due to slow and fast dynamics. We develop a coarse grid approximation based on the Generalized Multiscale Finite Element Method (GMsFEM), where we solve local spectral problems for construction of the multiscale basis functions. We present numerical results for the two-dimensional model problems in fractured heterogeneous porous media. We investigate error analysis between reference (fine-scale) solution and multiscale solution with different numbers of multiscale basis functions. The results show that the proposed method can provide good accuracy on a coarse grid.

show abstract

Section: Introductionmentioning

confidence: 99%

A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media

Tyrylgin¹,

Vasilyeva²,

Alikhanov³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…While this approach to the effective behavior of three-dimensional linearized elastic bodies is well-established, much less attention has been paid to the poroelastic thin bodies. As the recent example of the special issue of the journal Transport in Porous Media [34,19] shows, this is likely to change. Also there is a related experimental work, see [17].…”

Section: Introductionmentioning

confidence: 99%

Derivation of a poroelastic elliptic membrane shell model

Mikelić

Tambača

2018

Applicable Analysis

View full text Add to dashboard Cite

International audienceA derivation of the model for a poroelastic elliptic membrane shell is undertaken. The flow and deformation in a three-dimensional shell domain is described by the quasi-static Biot equations of linear poroelasticity. We consider the limit when the shell thickness goes to zero and look for the limit equations. Using the technique developed in the seminal articles by Ciarlet, Lods, Miara et al and the recent results on the rigorous derivation of the equations for poroelastic plates and flexural poroelastic shells by Marciniak-Czochra, Mikeli´cMikeli´c and Tambača, we present a rigorous derivation of the linear poroelastic elliptic membrane shell model. After rescaling, the corresponding velocity and the pressure field are close in the C([0, T ]; (H 1 x) 2 × (L 2 x) 2) norm and the stresses in C([0, T ]; (L 2 x) 9) norm. In the case of a spherical membrane shell we confirm the results by Taber from the literature

show abstract