Robust fixed stress splitting for Biot's equations in heterogeneous media

DOI10.1016/j.aml.2016.12.019zbMath1383.74025OpenAlexW2575247701MaRDI QIDQ518484

Jakub Wiktor Both, Kundan Kumar, Manuel Borregales, Jan Martin Nordbotten, Florin Adrian Radu

Publication date: 28 March 2017

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1956/21143

zbMATH Keywords

heterogeneous porous media iterative coupling Biot's equations linear poroelasticity

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Inhomogeneity in solid mechanics (74E05) Flows in porous media; filtration; seepage (76S05) Stress (74A10)

Related Items (56)

Performance studies of the fixed stress split algorithm for immiscible two-phase flow coupled with linear poromechanics ⋮ Well-posedness of the fully coupled quasi-static thermo-poroelastic equations with nonlinear convective transport ⋮ Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema ⋮ An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters ⋮ A two-stage preconditioner for multiphase poromechanics in reservoir simulation ⋮ Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media ⋮ IPACS: integrated phase-field advanced crack propagation simulator. An adaptive, parallel, physics-based-discretization phase-field framework for fracture propagation in porous media ⋮ Multiscale two-stage solver for Biot's poroelasticity equations in subsurface media ⋮ Some optimally convergent algorithms for decoupling the computation of Biot's model ⋮ Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media ⋮ Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials ⋮ Accuracy of fully coupled and sequential approaches for modeling hydro- and geomechanical processes ⋮ Mathematical effects of linear visco-elasticity in quasi-static Biot models ⋮ A priori error estimates of two monolithic schemes for Biot's consolidation model ⋮ An adaptive solution strategy for Richards' equation ⋮ Robust Block Preconditioners for Biot’s Model ⋮ Parameter-Robust Convergence Analysis of Fixed-Stress Split Iterative Method for Multiple-Permeability Poroelasticity Systems ⋮ Free Energy Diminishing Discretization of Darcy-Forchheimer Flow in Poroelastic Media ⋮ Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium ⋮ A partially parallel-in-time fixed-stress splitting method for Biot's consolidation model ⋮ Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media ⋮ A robust solution strategy for the Cahn-Larché equations ⋮ Monolithic and splitting solution schemes for fully coupled quasi-static thermo-poroelasticity with nonlinear convective transport ⋮ Robust Preconditioners for a New Stabilized Discretization of the Poroelastic Equations ⋮ Network-inspired versus Kozeny-Carman based permeability-porosity relations applied to Biot's poroelasticity model ⋮ Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics ⋮ On the Convergence of Flow and Mechanics Iterative Coupling Schemes in Fractured Heterogeneous Poro-Elastic Media ⋮ Iterative Coupling for Fully Dynamic Poroelasticity ⋮ Coupled Flow and Mechanics in a 3D Porous Media with Line Sources ⋮ The Fixed-Stress Splitting Scheme for Biot’s Equations as a Modified Richardson Iteration: Implications for Optimal Convergence ⋮ New stabilized discretizations for poroelasticity and the Stokes' equations ⋮ Adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of Biot's consolidation model ⋮ Virtual element methods for the three-field formulation of time-dependent linear poroelasticity ⋮ Iterative solvers for Biot model under small and large deformations ⋮ Approximate inverse-based block preconditioners in poroelasticity ⋮ A moving finite element framework for fast infiltration in nonlinear poroelastic media ⋮ Efficient solvers for hybridized three-field mixed finite element coupled poromechanics ⋮ Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem ⋮ Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems ⋮ Robust iterative schemes for non-linear poromechanics ⋮ A mixed three-node triangular element with continuous nodal stress for fully dynamic consolidation of porous media ⋮ Numerical solvers for a poromechanic problem with a moving boundary ⋮ The Correspondence between Voigt and Reuss Bounds and the Decoupling Constraint in a Two-Grid Staggered Algorithm for Consolidation in Heterogeneous Porous Media ⋮ Parameter-robust Uzawa-type iterative methods for double saddle point problems arising in Biot’s consolidation and multiple-network poroelasticity models ⋮ Iterative splitting schemes for a soft material poromechanics model ⋮ Space-time finite element approximation of the Biot poroelasticity system with iterative coupling ⋮ On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics ⋮ A linear domain decomposition method for partially saturated flow in porous media ⋮ A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics ⋮ Phase-field modeling through iterative splitting of hydraulic fractures in a poroelastic medium ⋮ Enhanced relaxed physical factorization preconditioner for coupled poromechanics ⋮ Convergence of single rate and multirate undrained split iterative schemes for a fractured Biot model ⋮ Reactive flows in deformable, complex media. Abstracts from the workshop held August 26 -- September 1, 2018 ⋮ Semi-explicit discretization schemes for weakly coupled elliptic-parabolic problems ⋮ Robust Preconditioners for Perturbed Saddle-Point Problems and Conservative Discretizations of Biot's Equations Utilizing Total Pressure ⋮ An iterative decoupled algorithm with unconditional stability for Biot model

Uses Software

DUNE

Cites Work

This page was built for publication: Robust fixed stress splitting for Biot's equations in heterogeneous media