Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

Castelletto, Nicola; Klevtsov, Sergey; Hajibeygi, Hadi; Tchelepi, Hamdi A.

doi:10.1007/s10596-018-9791-z

Title: Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

Journal Article · Fri Nov 09 00:00:00 EST 2018 · Computational Geosciences

DOI:https://doi.org/10.1007/s10596-018-9791-z· OSTI ID:1548341

Castelletto, Nicola ^[1]; Klevtsov, Sergey ^[2]; Hajibeygi, Hadi ^[3];

^[2]

Stanford Univ., CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Stanford Univ., CA (United States)
Delft Univ. of Technology (Netherlands)

In this paper, we propose a two-stage preconditioner for accelerating the iterative solution by a Krylov subspace method of Biot’s poroelasticity equations based on a displacement-pressure formulation. The spatial discretization combines a finite element method for mechanics and a finite volume approach for flow. The fully implicit backward Euler scheme is used for time integration. The result is a 2 × 2 block linear system for each timestep. The preconditioning operator is obtained by applying a two-stage scheme. The first stage is a global preconditioner that employs multiscale basis functions to construct coarse-scale coupled systems using a Galerkin projection. This global stage is effective at damping low-frequency error modes associated with long-range coupling of the unknowns. The second stage is a local block-triangular smoothing preconditioner, which is aimed at high-frequency error modes associated with short-range coupling of the variables. Lastly, various numerical experiments are used to demonstrate the robustness of the proposed solver.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1548341

Report Number(s):: LLNL-JRNL-747875; 932724

Journal Information:: Computational Geosciences, Vol. 23, Issue 2; ISSN 1420-0597

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 20 works

Citation information provided by
Web of Science

References (87)

A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems Bramble, James H.; Pasciak, Joseph E. Mathematics of Computation, Vol. 50, Issue 181 https://doi.org/10.1090/S0025-5718-1988-0917816-8	journal	January 1988
A nonconforming finite element method for the Biot’s consolidation model in poroelasticity Hu, Xiaozhe; Rodrigo, Carmen; Gaspar, Francisco J. Journal of Computational and Applied Mathematics, Vol. 310 https://doi.org/10.1016/j.cam.2016.06.003	journal	January 2017
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation Jenny, P.; Lee, S. H.; Tchelepi, H. A. Journal of Computational Physics, Vol. 187, Issue 1 https://doi.org/10.1016/S0021-9991(03)00075-5	journal	May 2003
On an Uzawa smoother in multigrid for poroelasticity equations: On an Uzawa smoother in multigrid for poroelasticity equations Luo, P.; Rodrigo, C.; Gaspar, F. J. Numerical Linear Algebra with Applications, Vol. 24, Issue 1 https://doi.org/10.1002/nla.2074	journal	November 2016
Parameter-Robust Discretization and Preconditioning of Biot's Consolidation Model Lee, Jeonghun J.; Mardal, Kent-Andre; Winther, Ragnar SIAM Journal on Scientific Computing, Vol. 39, Issue 1 https://doi.org/10.1137/15M1029473	journal	January 2017
Adaptive fully implicit multi-scale finite-volume method for multi-phase flow and transport in heterogeneous porous media Jenny, P.; Lee, S. H.; Tchelepi, H. A. Journal of Computational Physics, Vol. 217, Issue 2 https://doi.org/10.1016/j.jcp.2006.01.028	journal	September 2006
A coupling of mixed and continuous Galerkin finite element methods for poroelasticity II: the discrete-in-time case Phillips, Phillip Joseph; Wheeler, Mary F. Computational Geosciences, Vol. 11, Issue 2 https://doi.org/10.1007/s10596-007-9044-z	journal	March 2007
Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media Both, Jakub Wiktor; Kumar, Kundan; Nordbotten, Jan Martin Computers & Mathematics with Applications, Vol. 77, Issue 6 https://doi.org/10.1016/j.camwa.2018.07.033	journal	March 2019
Cell-centered finite volume discretizations for deformable porous media: CELL-CENTERED FINITE VOLUME DISCRETIZATIONS FOR ELASTICITY Nordbotten, Jan Martin International Journal for Numerical Methods in Engineering, Vol. 100, Issue 6 https://doi.org/10.1002/nme.4734	journal	August 2014
Two-way coupling in reservoir-geomechanical models: vertex-centered Galerkin geomechanical model cell-centered and vertex-centered finite volume reservoir models: COUPLING FINITE-VOLUME RESERVOIR AND GALERKIN PEOMECHANICAL MODELS Prevost, Jean H. International Journal for Numerical Methods in Engineering, Vol. 98, Issue 8 https://doi.org/10.1002/nme.4657	journal	March 2014
Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A. Journal of Computational Physics, Vol. 330 https://doi.org/10.1016/j.jcp.2016.11.010	journal	February 2017
An iterative solution method for linear systems of which the coefficient matrix is a symmetric $M$-matrix Meijerink, J. A.; van der Vorst, H. A. Mathematics of Computation, Vol. 31, Issue 137 https://doi.org/10.1090/S0025-5718-1977-0438681-4	journal	January 1977
Monotone nonlinear finite-volume method for challenging grids Schneider, M.; Flemisch, B.; Helmig, R. Computational Geosciences, Vol. 22, Issue 2 https://doi.org/10.1007/s10596-017-9710-8	journal	January 2018
Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps Spillane, N.; Dolean, V.; Hauret, P. Numerische Mathematik, Vol. 126, Issue 4 https://doi.org/10.1007/s00211-013-0576-y	journal	August 2013
Robust fixed stress splitting for Biot’s equations in heterogeneous media Both, Jakub Wiktor; Borregales, Manuel; Nordbotten, Jan Martin Applied Mathematics Letters, Vol. 68 https://doi.org/10.1016/j.aml.2016.12.019	journal	June 2017
A locally conservative finite element framework for the simulation of coupled flow and reservoir geomechanics Jha, Birendra; Juanes, Ruben Acta Geotechnica, Vol. 2, Issue 3 https://doi.org/10.1007/s11440-007-0033-0	journal	July 2007
Use of Multiple Multiscale Operators To Accelerate Simulation of Complex Geomodels Lie, Knut-Andreas; Møyner, Olav; Natvig, Jostein R. SPE Journal, Vol. 22, Issue 06 https://doi.org/10.2118/182701-PA	journal	December 2017
Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits Kim, J.; Tchelepi, H. A.; Juanes, R. Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 13-16 https://doi.org/10.1016/j.cma.2010.12.022	journal	March 2011
Convergence analysis of a new mixed finite element method for Biot's consolidation model Yi, Son-Young Numerical Methods for Partial Differential Equations, Vol. 30, Issue 4 https://doi.org/10.1002/num.21865	journal	February 2014
A fully coupled 3-D mixed finite element model of Biot consolidation Ferronato, Massimiliano; Castelletto, Nicola; Gambolati, Giuseppe Journal of Computational Physics, Vol. 229, Issue 12 https://doi.org/10.1016/j.jcp.2010.03.018	journal	June 2010
Convergence of iterative coupling for coupled flow and geomechanics Mikelić, Andro; Wheeler, Mary F. Computational Geosciences, Vol. 17, Issue 3 https://doi.org/10.1007/s10596-012-9318-y	journal	October 2012
Thermo-hydro-mechanical modeling of fluid geological storage by Godunov-mixed methods: THERMO-HYDRO-MECHANICAL MODELING BY GODUNOV-MIXED METHODS Castelletto, N.; Ferronato, M.; Gambolati, G. International Journal for Numerical Methods in Engineering https://doi.org/10.1002/nme.3352	journal	March 2012
Stability and monotonicity for some discretizations of the Biot’s consolidation model Rodrigo, C.; Gaspar, F. J.; Hu, X. Computer Methods in Applied Mechanics and Engineering, Vol. 298 https://doi.org/10.1016/j.cma.2015.09.019	journal	January 2016
Iterative Methods for Sparse Linear Systems Saad, Yousef https://doi.org/10.1137/1.9780898718003	book	January 2003
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems Saad, Youcef; Schultz, Martin H. SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3 https://doi.org/10.1137/0907058	journal	July 1986
Constrained pressure residual multiscale (CPR-MS) method for fully implicit simulation of multiphase flow in porous media Cusini, Matteo; Lukyanov, Alexander A.; Natvig, Jostein Journal of Computational Physics, Vol. 299 https://doi.org/10.1016/j.jcp.2015.07.019	journal	October 2015
A multiscale fixed stress split iterative scheme for coupled flow and poromechanics in deep subsurface reservoirs Dana, Saumik; Ganis, Benjamin; Wheeler, Mary F. Journal of Computational Physics, Vol. 352 https://doi.org/10.1016/j.jcp.2017.09.049	journal	January 2018
A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system Gaspar, F. J.; Lisbona, F. J.; Oosterlee, C. W. Numerical Linear Algebra with Applications, Vol. 11, Issue 23 https://doi.org/10.1002/nla.372	journal	March 2004
Finite volume methods for elasticity with weak symmetry: FINITE VOLUME METHODS FOR ELASTICITY WITH WEAK SYMMETRY Keilegavlen, Eirik; Nordbotten, Jan Martin International Journal for Numerical Methods in Engineering, Vol. 112, Issue 8 https://doi.org/10.1002/nme.5538	journal	April 2017
New stabilized discretizations for poroelasticity and the Stokes’ equations Rodrigo, C.; Hu, X.; Ohm, P. Computer Methods in Applied Mechanics and Engineering, Vol. 341 https://doi.org/10.1016/j.cma.2018.07.003	journal	November 2018
Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media Cusini, Matteo; Fryer, Barnaby; van Kruijsdijk, Cor Journal of Computational Physics, Vol. 354 https://doi.org/10.1016/j.jcp.2017.10.052	journal	February 2018
Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method Kalchev, D. Z.; Lee, C. S.; Villa, U. SIAM Journal on Scientific Computing, Vol. 38, Issue 5 https://doi.org/10.1137/15M1036683	journal	January 2016
Scalable algorithms for three-field mixed finite element coupled poromechanics Castelletto, Nicola; White, Joshua A.; Ferronato, Massimiliano Journal of Computational Physics, Vol. 327 https://doi.org/10.1016/j.jcp.2016.09.063	journal	December 2016
On the causes of pressure oscillations in low-permeable and low-compressible porous media: PRESSURE OSCILLATIONS IN LOW-PERMEABLE POROUS MEDIA Haga, Joachim Berdal; Osnes, Harald; Langtangen, Hans Petter International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 36, Issue 12 https://doi.org/10.1002/nag.1062	journal	July 2011
On the relationship between the multiscale finite-volume method and domain decomposition preconditioners Nordbotten, J. M.; Bjørstad, P. E. Computational Geosciences, Vol. 12, Issue 3 https://doi.org/10.1007/s10596-007-9066-6	journal	January 2008
Block-preconditioned Krylov Methods for Coupled Multiphase Reservoir Flow and Geomechanics Klevtsov, S.; Castelletto, N.; White, J. A. ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery, Proceedings https://doi.org/10.3997/2214-4609.201601900	conference	August 2016
Adaptive algebraic multiscale solver for compressible flow in heterogeneous porous media Ţene, Matei; Wang, Yixuan; Hajibeygi, Hadi Journal of Computational Physics, Vol. 300 https://doi.org/10.1016/j.jcp.2015.08.009	journal	November 2015
Coupled multiphase flow and poromechanics: A computational model of pore pressure effects on fault slip and earthquake triggering Jha, Birendra; Juanes, Ruben Water Resources Research, Vol. 50, Issue 5 https://doi.org/10.1002/2013WR015175	journal	May 2014
Multiscale finite element coarse spaces for the application to linear elasticity Buck, Marco; Iliev, Oleg; Andrä, Heiko Open Mathematics, Vol. 11, Issue 4 https://doi.org/10.2478/s11533-012-0166-8	journal	January 2013
A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids Møyner, Olav; Lie, Knut-Andreas Journal of Computational Physics, Vol. 304 https://doi.org/10.1016/j.jcp.2015.10.010	journal	January 2016
A Coupled Reservoir and Geomechanical Simulation System Settari, Antonin; Mourits, F. M. SPE Journal, Vol. 3, Issue 03 https://doi.org/10.2118/50939-PA	journal	September 1998
Iterative multiscale finite-volume method Hajibeygi, Hadi; Bonfigli, Giuseppe; Hesse, Marc Andre Journal of Computational Physics, Vol. 227, Issue 19 https://doi.org/10.1016/j.jcp.2008.06.013	journal	October 2008
Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques Christie, M. A.; Blunt, M. J. SPE Reservoir Evaluation & Engineering, Vol. 4, Issue 04 https://doi.org/10.2118/72469-PA	journal	August 2001
A reduced order model-based preconditioner for the efficient solution of transient diffusion equations: A ROM-BASED PRECONDITIONER FOR TRANSIENT DIFFUSION PDES Pasetto, Damiano; Ferronato, Massimiliano; Putti, Mario International Journal for Numerical Methods in Engineering, Vol. 109, Issue 8 https://doi.org/10.1002/nme.5320	journal	July 2016
Large scale micro finite element analysis of 3D bone poroelasticity Turan, Erhan; Arbenz, Peter Parallel Computing, Vol. 40, Issue 7 https://doi.org/10.1016/j.parco.2013.09.002	journal	July 2014
A Time-Stepping Scheme for Coupled Reservoir Flow and Geomechanics Gai, Xiuli; Sun, Shuyu; Wheeler, Mary Fanett SPE Annual Technical Conference and Exhibition https://doi.org/10.2118/97054-MS	conference	April 2013
Monotone multiscale finite volume method Wang, Yixuan; Hajibeygi, Hadi; Tchelepi, Hamdi A. Computational Geosciences, Vol. 20, Issue 3 https://doi.org/10.1007/s10596-015-9506-7	journal	August 2015
Block-preconditioned Newton–Krylov solvers for fully coupled flow and geomechanics White, Joshua A.; Borja, Ronaldo I. Computational Geosciences, Vol. 15, Issue 4 https://doi.org/10.1007/s10596-011-9233-7	journal	April 2011
Finite volume schemes for diffusion equations: Introduction to and review of modern methods Droniou, Jerome Mathematical Models and Methods in Applied Sciences, Vol. 24, Issue 08 https://doi.org/10.1142/S0218202514400041	journal	May 2014
Two-Stage Algebraic Multiscale Linear Solver for Highly Heterogeneous Reservoir Models Zhou, Hui; Tchelepi, Hamdi A. SPE Journal, Vol. 17, Issue 02 https://doi.org/10.2118/141473-PA	journal	June 2012
A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case Phillips, Phillip Joseph; Wheeler, Mary F. Computational Geosciences, Vol. 11, Issue 2 https://doi.org/10.1007/s10596-007-9045-y	journal	March 2007
Successful Application of Multiscale Methods in a Real Reservoir Simulator Environment Lie, K. A.; Møyner, O.; Natvig, J. R. ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery, Proceedings https://doi.org/10.3997/2214-4609.201601893	conference	August 2016
Stable Cell-Centered Finite Volume Discretization for Biot Equations Nordbotten, Jan Martin SIAM Journal on Numerical Analysis, Vol. 54, Issue 2 https://doi.org/10.1137/15M1014280	journal	January 2016
Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations Bergamaschi, Luca; Ferronato, Massimiliano; Gambolati, Giuseppe Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 25-28 https://doi.org/10.1016/j.cma.2007.01.013	journal	May 2007
Numerical solution of saddle point problems Benzi, Michele; Golub, Gene H.; Liesen, Jörg Acta Numerica, Vol. 14 https://doi.org/10.1017/S0962492904000212	journal	April 2005
A generalized multiscale finite element method for poroelasticity problems II: Nonlinear coupling Brown, Donald L.; Vasilyeva, Maria Journal of Computational and Applied Mathematics, Vol. 297 https://doi.org/10.1016/j.cam.2015.11.007	journal	May 2016
A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media Hou, Thomas Y.; Wu, Xiao-Hui Journal of Computational Physics, Vol. 134, Issue 1 https://doi.org/10.1006/jcph.1997.5682	journal	June 1997
Algebraic multiscale solver for flow in heterogeneous porous media Wang, Yixuan; Hajibeygi, Hadi; Tchelepi, Hamdi A. Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.11.024	journal	February 2014
TP or not TP, that is the question Eymard, R.; Gallouët, T.; Guichard, C. Computational Geosciences, Vol. 18, Issue 3-4 https://doi.org/10.1007/s10596-013-9392-9	journal	January 2014
Multigrid method for nonlinear poroelasticity equations Luo, P.; Rodrigo, C.; Gaspar, F. J. Computing and Visualization in Science, Vol. 17, Issue 5 https://doi.org/10.1007/s00791-016-0260-8	journal	October 2015
A Real-Field Multiscale Black-Oil Reservoir Simulator Kozlova, A.; Li, Z.; Natvig, J. R. SPE Reservoir Simulation Symposium https://doi.org/10.2118/173226-MS	conference	February 2015
Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics: Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics Castelletto, N.; White, J. A.; Tchelepi, H. A. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 39, Issue 14 https://doi.org/10.1002/nag.2400	journal	June 2015
A parallel block preconditioner for large-scale poroelasticity with highly heterogeneous material parameters Haga, Joachim Berdal; Osnes, Harald; Langtangen, Hans Petter Computational Geosciences, Vol. 16, Issue 3 https://doi.org/10.1007/s10596-012-9284-4	journal	March 2012
Multiscale model reduction for shale gas transport in poroelastic fractured media Akkutlu, I. Yucel; Efendiev, Yalchin; Vasilyeva, Maria Journal of Computational Physics, Vol. 353 https://doi.org/10.1016/j.jcp.2017.10.023	journal	January 2018
On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics Gaspar, Francisco J.; Rodrigo, Carmen Computer Methods in Applied Mechanics and Engineering, Vol. 326 https://doi.org/10.1016/j.cma.2017.08.025	journal	November 2017
RMCP: Relaxed Mixed Constraint Preconditioners for saddle point linear systems arising in geomechanics Bergamaschi, Luca; Martínez, Ángeles Computer Methods in Applied Mechanics and Engineering, Vol. 221-222 https://doi.org/10.1016/j.cma.2012.02.004	journal	May 2012
Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS) Ţene, Matei; Al Kobaisi, Mohammed Saad; Hajibeygi, Hadi Journal of Computational Physics, Vol. 321 https://doi.org/10.1016/j.jcp.2016.06.012	journal	September 2016
Multiscale finite-element method for linear elastic geomechanics Castelletto, Nicola; Hajibeygi, Hadi; Tchelepi, Hamdi A. Journal of Computational Physics, Vol. 331 https://doi.org/10.1016/j.jcp.2016.11.044	journal	February 2017
Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients White, Joshua A.; Borja, Ronaldo I. Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 49-50 https://doi.org/10.1016/j.cma.2008.05.015	journal	September 2008
On stability and convergence of finite element approximations of Biot's consolidation problem Murad, Márcio A.; Loula, Abimael F. D. International Journal for Numerical Methods in Engineering, Vol. 37, Issue 4 https://doi.org/10.1002/nme.1620370407	journal	February 1994
Space–time finite element approximation of the Biot poroelasticity system with iterative coupling Bause, M.; Radu, F. A.; Köcher, U. Computer Methods in Applied Mechanics and Engineering, Vol. 320 https://doi.org/10.1016/j.cma.2017.03.017	journal	June 2017
Hybrid Multiscale Formulation for Coupled Flow and Geomechanics Castelletto, N.; Hajibeygi, H.; Tchelepi, H. A. ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery, Proceedings https://doi.org/10.3997/2214-4609.201601888	conference	August 2016
Preconditioning Techniques for Large Linear Systems: A Survey Benzi, Michele Journal of Computational Physics, Vol. 182, Issue 2 https://doi.org/10.1006/jcph.2002.7176	journal	November 2002
A Generalized Multiscale Finite Element Method for poroelasticity problems I: Linear problems Brown, Donald L.; Vasilyeva, Maria Journal of Computational and Applied Mathematics, Vol. 294 https://doi.org/10.1016/j.cam.2015.08.007	journal	March 2016
Stability, Accuracy, and Efficiency of Sequential Methods for Coupled Flow and Geomechanics Kim, Jihoon; Tchelepi, Hamdi A.; Juanes, Ruben SPE Journal, Vol. 16, Issue 02 https://doi.org/10.2118/119084-PA	journal	June 2011
Block-partitioned solvers for coupled poromechanics: A unified framework White, Joshua A.; Castelletto, Nicola; Tchelepi, Hamdi A. Computer Methods in Applied Mechanics and Engineering, Vol. 303 https://doi.org/10.1016/j.cma.2016.01.008	journal	May 2016
Coupling multiscale finite element method for consolidation analysis of heterogeneous saturated porous media Zhang, H. W.; Fu, Z. D.; Wu, J. K. Advances in Water Resources, Vol. 32, Issue 2 https://doi.org/10.1016/j.advwatres.2008.11.002	journal	February 2009
Successful application of multiscale methods in a real reservoir simulator environment Lie, K. -A.; Møyner, O.; Natvig, J. R. Computational Geosciences, Vol. 21, Issue 5-6 https://doi.org/10.1007/s10596-017-9627-2	journal	March 2017
A Locally Conservative Finite Element Framework for the Simulation of Coupled Flow and Reservoir Geomechanics Juanes, Ruben; Jha, Birendra SPE Annual Technical Conference and Exhibition, All Days https://doi.org/10.2118/102812-ms	conference	September 2006
An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix Meijerink, J. A.; van der Vorst, H. A. Mathematics of Computation, Vol. 31, Issue 137 https://doi.org/10.2307/2005786	journal	January 1977
Two-Stage Algebraic Multiscale Linear Solver for Highly Heterogeneous Reservoir Models Zhou, H. .; Tchelepi, H. A. SPE Reservoir Simulation Symposium, All Days https://doi.org/10.2118/141473-ms	conference	February 2011
Finite volume schemes for diffusion equations: introduction to and review of modern methods Droniou, Jerome arXiv https://doi.org/10.48550/arxiv.1407.1567	text	January 2014
A Generalized Multiscale Finite Element Method for Poroelasticity Problems I: Linear Problems Brown, Donald L.; Vasilyeva, Maria arXiv https://doi.org/10.48550/arxiv.1508.02136	preprint	January 2015
Stable cell-centered finite volume discretization for Biot equations Nordbotten, Jan Martin arXiv https://doi.org/10.48550/arxiv.1510.01695	text	January 2015
Adaptive Algebraic Multiscale Solver for Compressible Flow in Heterogeneous Porous Media Tene, Matei; Wang, Yixuan; Hajibeygi, Hadi arXiv https://doi.org/10.48550/arxiv.1705.05783	text	January 2017
Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS) Tene, Matei; Kobaisi, Mohammed Saad Al; Hajibeygi, Hadi arXiv https://doi.org/10.48550/arxiv.1705.05784	text	January 2017
Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media Both, Jakub Wiktor; Kumar, Kundan; Nordbotten, Jan Martin arXiv https://doi.org/10.48550/arxiv.1805.04211	text	January 2018

Cited By (1)

On the optimization of the fixed‐stress splitting for Biot's equations Storvik, Erlend; Both, Jakub W.; Kumar, Kundan International Journal for Numerical Methods in Engineering, Vol. 120, Issue 2 https://doi.org/10.1002/nme.6130	journal	June 2019

Similar Records

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Journal Article · Tue Feb 15 00:00:00 EST 2022 · SIAM Journal on Scientific Computing · OSTI ID:1548341

Southworth, Ben S.; Krzysik, Oliver; Pazner, Will; +1 more

Preconditioning a Newton-Krylov solver for all-speed melt pool flow physics

Journal Article · Thu Jul 25 00:00:00 EDT 2019 · Journal of Computational Physics · OSTI ID:1548341

Weston, Brian; Nourgaliev, Robert; Delplanque, Jean -Pierre; +1 more

A coupled multipoint stress–multipoint flux mixed finite element method for the Biot system of poroelasticity

Journal Article · Mon Sep 28 00:00:00 EDT 2020 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:1548341

Ambartsumyan, Ilona; Khattatov, Eldar; Yotov, Ivan

Related Subjects

58 GEOSCIENCES
97 MATHEMATICS AND COMPUTING
Poromechanics
Multiscale methods
Preconditioners
Iterative methods

Title: Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

Citation Formats

References (87)

Cited By (1)

Similar Records

Related Subjects