Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics
Abstract
Here, the paper deals with the numerical solution of Biot's equations of coupled consolidation obtained by a mixed formulation combining continuous Galerkin finite–element and multipoint flux approximation finite–volume methods. The solution algorithm relies on the recently developed fixed–stress solution scheme, in which first the flow problem and then the mechanical one are addressed iteratively. We show that the algorithm can be interpreted as a particular block triangular preconditioning strategy applied within a Richardson iteration. The key component to the success of the preconditioner is the sparse approximation to the Schur complement based on a pressure space mass matrix scaled by a weighting factor that depends element–wise on the inverse of a suitable bulk modulus. The accuracy of the method is assessed, making use of well–known analytical solutions from the literature. Numerical results demonstrate robustness and low computational cost of the fixed–stress scheme in accurately capturing the two–way coupling between deformation and pressure.
- Authors:
-
- Stanford Univ., Stanford, CA (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1463026
- Report Number(s):
- LLNL-JRNL-737002
Journal ID: ISSN 0363-9061; 889943
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- International Journal for Numerical and Analytical Methods in Geomechanics
- Additional Journal Information:
- Journal Volume: 39; Journal Issue: 14; Journal ID: ISSN 0363-9061
- Publisher:
- Wiley
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; poromechanics; iterative fixed-stress scheme; finite element; multipoint flux approximation
Citation Formats
Castelletto, N., White, J. A., and Tchelepi, H. A.. Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics. United States: N. p., 2015.
Web. https://doi.org/10.1002/nag.2400.
Castelletto, N., White, J. A., & Tchelepi, H. A.. Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics. United States. https://doi.org/10.1002/nag.2400
Castelletto, N., White, J. A., and Tchelepi, H. A.. Mon .
"Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics". United States. https://doi.org/10.1002/nag.2400. https://www.osti.gov/servlets/purl/1463026.
@article{osti_1463026,
title = {Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics},
author = {Castelletto, N. and White, J. A. and Tchelepi, H. A.},
abstractNote = {Here, the paper deals with the numerical solution of Biot's equations of coupled consolidation obtained by a mixed formulation combining continuous Galerkin finite–element and multipoint flux approximation finite–volume methods. The solution algorithm relies on the recently developed fixed–stress solution scheme, in which first the flow problem and then the mechanical one are addressed iteratively. We show that the algorithm can be interpreted as a particular block triangular preconditioning strategy applied within a Richardson iteration. The key component to the success of the preconditioner is the sparse approximation to the Schur complement based on a pressure space mass matrix scaled by a weighting factor that depends element–wise on the inverse of a suitable bulk modulus. The accuracy of the method is assessed, making use of well–known analytical solutions from the literature. Numerical results demonstrate robustness and low computational cost of the fixed–stress scheme in accurately capturing the two–way coupling between deformation and pressure.},
doi = {10.1002/nag.2400},
journal = {International Journal for Numerical and Analytical Methods in Geomechanics},
number = 14,
volume = 39,
place = {United States},
year = {2015},
month = {6}
}
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