A stabilized element-based finite volume method for poroelastic problems

Honório, Hermínio Tasinafo; Maliska, Clóvis R.; Ferronato, Massimiliano; Janna, Carlo

doi:10.1016/j.jcp.2018.03.010

Cited by 26 publications

(10 citation statements)

References 29 publications

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“…Another strategy to solve (16) relies on using an appropriate projection operator. In particular, the idea is to project the system (16) onto the space Z = Ran(F), so as to annihilate the components of w lying in the kernel of F T .…”

Section: Methodsmentioning

confidence: 99%

“…However, this discretization does not intrinsically satisfy the inf-sup stability in the undrained limit [13,14]. Proper stabilization strategies, such as those recently advanced in [15][16][17][18][19][20], can be introduced to eliminate spurious oscillation modes in the pressure solution in undrained configurations, with minor changes to the algebraic structure of the problem (1).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics

Frigo¹,

Castelletto²,

Ferronato³

2019

SIAM J. Sci. Comput.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics

Frigo¹,

Castelletto²,

Ferronato³

2019

SIAM J. Sci. Comput.

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“…Solution of coupled HM processes can be handled analytically for simple geometries [22,23]. However, for complex geometries and non-homogeneous boundary conditions, we could use numerical approximations such as finite volume discretization [24,25,26] and finite element methods [27,28,29,30,31,32,33,34]. Recently, the possibility of solving linear elasticity problems and coupled HM processes using physics-informed neural networks is also presented in [35,36,37,38].…”

Section: Introductionmentioning

confidence: 99%

Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation

2021

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A simulation tool capable of speeding up the calculation for linear poroelasticity problems in heterogeneous porous media is of large practical interest for engineers, in particular, to effectively perform sensitivity analyses, uncertainty quantification, optimization, or control operations on the fluid pressure and bulk deformation fields. Towards this goal, we present here a non-intrusive model reduction framework using proper orthogonal decomposition (POD) and neural networks, based on the usual offline-online paradigm. As the conductivity of porous media can be highly heterogeneous and span several orders of magnitude, we utilize the interior penalty discontinuous Galerkin (DG) method as a full order solver to handle discontinuity and ensure local mass conservation during the offline stage. We then use POD as a data compression tool and compare the nested POD technique, in which time and uncertain parameter domains are compressed consecutively, to the classical POD method in which all domains are compressed simultaneously. The neural networks are finally trained to map the set of uncertain parameters, which could correspond to material properties, boundary conditions, or geometric characteristics, to the collection of coefficients calculated from an L 2 projection over the reduced basis. We then perform a non-intrusive evaluation of the neural networks to obtain coefficients corresponding to new values of the uncertain parameters during the online stage. We show that our framework provides reasonable approximations of the DG solution, but it is significantly faster. Moreover, the reduced order framework can capture sharp discontinuities of both displacement and pressure fields resulting from the heterogeneity in the media conductivity, which is generally challenging for intrusive reduced order methods. The sources of error are presented, showing that the nested POD technique is computationally advantageous and still provides comparable accuracy to the classical POD method. We also explore the effect of different choices of the hyperparameters of the neural network on the framework performance.Keywords poroelasticity • reduced order modeling • neural networks • discontinuous Galerkin • heterogeneity • finite element

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“…A fully-implicit time integration strategy is adopted, where all unknown fields are updated simultaneously in a monolithic manner [34,35]. A variety of finite-element and finite-volume based discretization strategies may be applied to these equations, each with certain advantages [36][37][38][39][40][41][42][43][44]. Of specific interest here, however, is a frequent choice: continuous trilinear interpolation for the displacement unknowns and element-wise constant fields for the pressure and saturation unknowns.…”

Section: Introductionmentioning

confidence: 99%

“…The schemes above were primarily developed for fluid mechanics problems. Since then, many of these stabilization schemes have been successfully applied to poromechanics with single-phase flow [42,[56][57][58][59][60][61]. However, the study of stabilization procedures addressing multiphase problems is still incipient, with just a few studies available [62,63].…”

Section: Introductionmentioning

confidence: 99%

A macroelement stabilization for multiphase poromechanics

Camargo,

White,

Borja

2019

Preprint

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Strong coupling between geomechanical deformation and multiphase fluid flow appears in a variety of geoscience applications. A common discretization strategy for these problems is a continuous Galerkin finite element scheme for the momentum balance equations and a finite volume scheme for the mass balance equations. When applied within a fully-implicit solution strategy, however, this discretization is not intrinsically stable. In the limit of small time steps or low permeabilities, spurious oscillations in the pressure field, i.e. checkerboarding, may be observed. Further, eigenvalues associated with the spurious modes will control the conditioning of the matrices and can dramatically degrade the convergence rate of iterative linear solvers. Here, we propose a stabilization technique in which the balance of mass equations are supplemented with stabilizing flux terms on a macroelement basis. The additional stabilization terms are dependent on a stabilization parameter. We identify an optimal value for this parameter using an analysis of the eigenvalue distribution of the macroelement Schur complement matrix. The resulting method is simple to implement and preserves the underlying sparsity pattern of the original discretization. Another appealing feature of the method is that mass is exactly conserved on macroelements, despite the addition of artificial fluxes. The efficacy of the proposed technique is demonstrated with several numerical examples.

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A stabilized element-based finite volume method for poroelastic problems

Cited by 26 publications

References 29 publications

A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics

A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics

Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation

A macroelement stabilization for multiphase poromechanics

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