Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media

Both, Jakub Wiktor; Kumar, Kundan; Nordbotten, Jan Martin; Radu, F.

doi:10.1016/j.camwa.2018.07.033

Cited by 66 publications

(57 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We mention that the fixed‐stress splitting scheme also can be applied to more involved extensions of Biot's equations, for example, including nonlinear water compressibility, unsaturated poroelasticity, the multiple‐network poroelasticity theory, finite‐strain poroplasticity, fractured porous media, and fracture propagation . For nonlinear problems, one combines a linearization technique, eg, the L ‐scheme, with the splitting algorithm; the convergence of the resulting scheme can be proved rigorously . Finally, we would like to mention some valuable variants of the fixed‐stress splitting scheme: the multirate fixed‐stress method, the multiscale fixed‐stress method, and the parallel‐in‐time fixed‐stress method …”

Section: Introductionmentioning

confidence: 99%

“…We mention that the fixed-stress splitting scheme also can be applied to more involved extensions of Biot's equations, for example, including nonlinear water compressibility, 32 unsaturated poroelasticity, 33,34 the multiple-network poroelasticity theory, 35,36 finite-strain poroplasticity, 37 fractured porous media, 38 and fracture propagation. 39,40 For nonlinear problems, one combines a linearization technique, eg, the L-scheme, 41,42 with the splitting algorithm; the convergence of the resulting scheme can be proved rigorously.…”

Section: Introductionmentioning

confidence: 99%

“…39,40 For nonlinear problems, one combines a linearization technique, eg, the L-scheme, 41,42 with the splitting algorithm; the convergence of the resulting scheme can be proved rigorously. 32,33 Finally, we would like to mention some valuable variants of the fixed-stress splitting scheme: the multirate fixed-stress method, 43 the multiscale fixed-stress method, 29 and the parallel-in-time fixed-stress method. 44 This paper is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the optimization of the fixed‐stress splitting for Biot's equations

Storvik

Both

Kumar

et al. 2019

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Summary In this work, we are interested in efficiently solving the quasi‐static, linear Biot model for poroelasticity. We consider the fixed‐stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well known that the convergence properties of the method strongly depend on the applied stabilization/tuning parameter. We show theoretically that, in addition to depending on the mechanical properties of the porous medium and the coupling coefficient, they also depend on the fluid flow and spatial discretization properties. The type of analysis presented in this paper is not restricted to a particular spatial discretization, although it is required to be inf‐sup stable with respect to the displacement‐pressure formulation. Furthermore, we propose a way to optimize this parameter that relies on the mesh independence of the scheme's optimal stabilization parameter. Illustrative numerical examples show that using the optimized stabilization parameter can significantly reduce the number of iterations.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the optimization of the fixed‐stress splitting for Biot's equations

Storvik

Both

Kumar

et al. 2019

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, the second approach has received interest for its higher precision in terms of fluid flux Li et al [19], Wheeler and Gai [24], da Silva et al [59], Both et al [63]. Before introducing the spatial discretization, consider a partition T H = {Ω e } of the domain Ω by convex elements.…”

Section: Spatial and Temporal Discretizationmentioning

confidence: 99%

An enhanced sequential fully implicit scheme for reservoir geomechanics

et al. 2020

View full text Add to dashboard Cite

In this paper, it is proposed an enhanced sequential fully implicit ESFI algorithm with a fixed stress split to approximate robustly poro-elastoplastic solutions related to reservoir geomechanics. The constitutive model considers the total strain effect on porosity/permeability variation and associative plasticity. The sequential fully implicit algorithm SFI is a popular solution to approximate solutions of a coupled system. Generally, the SFI consists of an outer loop to solve the coupled system, in which there are two inner iterative loops for each equation to implicitly solve the equations. The SFI algorithm occasionally suffers from slow convergence or even convergence failure. In order to improve the convergence (robustness) associated with SFI, a new nonlinear acceleration technique is proposed employing Shanks transformations in vector-valued variables to enhance the outer loop convergence, with a Quasi-Newton method considering the modified Thomas method for the internal loops. In this ESFI algorithm, the fluid flow formulation is defined by Darcy's law including nonlinear permeability based on Petunin model. The rock deformation includes a linear part being analyzed based on Biot's theory and a nonlinear part being established using Mohr-Coulomb associative plasticity for geomechanics. Temporal derivatives are approximated by an implicit Euler method and spatial discretizations are adopted using finite element in two different formulations. For the spatial discretization, two weak statements are obtained: the first one uses a continuous Galerkin for poro-elastoplastic and Darcy's flow; the second one uses a continuous Galerkin for poro-elastoplastic and a mixed finite element for Darcy's flow. Several numerical simulations are presented to evaluate the efficiency of ESFI algorithm in reducing the number of iterations. Distinct poromechanical problems in 1D, 2D, and 3D are approximated with linear and nonlinear settings. Where appropriate, the results were verified with analytic solutions and approximated solutions with an explicit Runge-Kutta solver for 2D axisymmetric poroelastoplastic problems.

show abstract

“…Some authors have recently started investigating facecentered and cell-centered finite-volume methods also for the mechanical subproblem [50][51][52][53][54] to account for mechanical effects when flow processes are of predominant importance. Also, in the context of single-phase poromechanics, locally mass-conservative approaches have been proposed using mixed three-field (displacement-velocity-pressure) or four-field (stress tensor-displacement-velocity-pressure) formulations, respectively [e.g., 27,29,30,[55][56][57][58][59][60][61][62][63][64][65][66].…”

Section: Discrete Formulationmentioning

confidence: 99%

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

White

Castelletto

Klevtsov

et al. 2019

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Many applications involving porous media-notably reservoir engineering and geologic applications-involve tight coupling between multiphase fluid flow, transport, and poromechanical deformation. While numerical models for these processes have become commonplace in research and industry, the poor scalability of existing solution algorithms has limited the size and resolution of models that may be practically solved. In this work, we propose a two-stage Newton-Krylov solution algorithm to address this shortfall. The proposed solver exhibits rapid convergence, good parallel scalability, and is robust in the presence of highly heterogeneous material properties. The key to success of the solver is a block-preconditioning strategy that breaks the fully-coupled system of mass and momentum balance equations into simpler sub-problems that may be readily addressed using targeted algebraic methods. Numerical results are presented to illustrate the performance of the solver on challenging benchmark problems.

show abstract

Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media

Cited by 66 publications

References 39 publications

On the optimization of the fixed‐stress splitting for Biot's equations

On the optimization of the fixed‐stress splitting for Biot's equations

An enhanced sequential fully implicit scheme for reservoir geomechanics

A two-stage preconditioner for multiphase poromechanics in reservoir simulation

Contact Info

Product

Resources

About