Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

By Ji-hoon Kim, Hamdi A. Tchelepi, Ruben Juanes. 2011

409 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c9445269fc11d8ed84208908c266fd9f67bba42d

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

On the optimization of the fixed‐stress splitting for Biot's equations (2018, neutral): “From (20) and (21) and the Cauchy-Schwarz inequality, we immediately obtain”
Accuracy and convergence properties of the fixed‐stress iterative solution of two‐way coupled poromechanics (2015, methodology): “This result confirms the recommendations made in [32] concerning the selection of the appropriate Q K.”
Stability and convergence of sequential methods for coupled flow and geomechanics: Drained and undrained splits (2011, methodology): “In a separate paper [73], we investigate another type of sequential methods, in which the flow step is solved first.”
Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium (2016, background): “More recently, Mikelić and Wheeler [23] have considered di↵erent iterative schemes for flow and mechanics couplings and established contractive results in suitable norms; see also [18, 19] for studying the stability of iterative algorithms.”
Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics (2016, methodology): “[14, 15] have used von Neumann stability analysis to study the stability and convergence of similar schemes.”
A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain (2013, methodology): “By using equal-order integration, we establish monolithically coupled poromechanics finite element models with less degrees of freedom, fewer integration points, and simpler data structures but without the necessity to design complex splitting I/O algorithms required for sequential coupling schemes ”