Iterative coupling schemes for mixed-dimensional poromechanical models with frictional contact: convergence analysis and adaptive stabilization
Abstract
This work addresses iterative coupling strategies for mixed-dimensional poromechanical models involving nonlinear frictional contact. Such models are essential for understanding fault reactivation processes in applications like geothermal energy extraction and CO2 storage, where fracture slip can induce leakage or seismicity. We analyze the convergence of fixed-point coupling schemes, namely the Undrained Split and Fixed-Stress algorithms, used to iteratively couple the mechanics and flow subproblems in quasi-static poromechanics. For linear contact-mechanical models, based on spectral analysis, we derive convergence rate estimates depending on stabilization parameters for the matrix and fault/fracture and two Rayleigh quotients related to the divergence and jump coupling operators. Optimal stabilization parameters are obtained by minimizing the convergence rate estimate. The convergence analysis is then extended to a class of nonlinear monotone contact models including normal compliance or non-penetration combined with either frictionless or Tresca friction. Nevertheless, both from analytical and numerical perspectives, fixed stabilization parameters fail to ensure convergence in the case of Coulomb friction or shear dilation terms. To address these limitations, we investigate adaptive stabilization through probing or/and Anderson acceleration. Numerical experiments confirm the theoretical predictions and demonstrate significant improvements in efficiency and robustness with adaptive stabilization for nonlinear fracture opening and sliding.
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BibTeX
@misc{jonval2026iterative,
title = {{Iterative coupling schemes for mixed-dimensional poromechanical models with frictional contact: convergence analysis and adaptive stabilization}},
author = {Maxime Jonval and Roland Masson and Guillaume Enchéry},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05747360v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Iterative coupling schemes for mixed-dimensional poromechanical models with frictional contact: convergence analysis and adaptive stabilization
AU - Maxime Jonval
AU - Roland Masson
AU - Guillaume Enchéry
PY - 2026
DA - 2026/09/11
PB - HAL
UR - https://hal.science/hal-05747360v1
AB - This work addresses iterative coupling strategies for mixed-dimensional poromechanical models involving nonlinear frictional contact. Such models are essential for understanding fault reactivation processes in applications like geothermal energy extraction and CO2 storage, where fracture slip can induce leakage or seismicity. We analyze the convergence of fixed-point coupling schemes, namely the Undrained Split and Fixed-Stress algorithms, used to iteratively couple the mechanics and flow subproblems in quasi-static poromechanics. For linear contact-mechanical models, based on spectral analysis, we derive convergence rate estimates depending on stabilization parameters for the matrix and fault/fracture and two Rayleigh quotients related to the divergence and jump coupling operators. Optimal stabilization parameters are obtained by minimizing the convergence rate estimate. The convergence analysis is then extended to a class of nonlinear monotone contact models including normal compliance or non-penetration combined with either frictionless or Tresca friction. Nevertheless, both from analytical and numerical perspectives, fixed stabilization parameters fail to ensure convergence in the case of Coulomb friction or shear dilation terms. To address these limitations, we investigate adaptive stabilization through probing or/and Anderson acceleration. Numerical experiments confirm the theoretical predictions and demonstrate significant improvements in efficiency and robustness with adaptive stabilization for nonlinear fracture opening and sliding.
ER -