Unconditionally stable sequential schemes for all-way coupled thermoporomechanics: Undrained-adiabatic and extended fixed-stress splits
Abstract
In this work, we propose two sequential methods for the all-way coupled thermoporomechanical problems: the undrained-adiabatic split that combines together the undrained and adiabatic methods of poromechanics and thermomechanics, respectively, and the extended fixed-stress split. We perform nonlinear stability analysis for the two sequential methods, introducing a new extended norm that can encompass the all-way coupled thermoporomechanical problems. We find that the two sequential methods are unconditionally stable if α ≥ 0.5, where α is the parameter of time discretization for the generalized midpoint rule at tn+α. We also perform the spectral analysis in order to further investigate stability and convergence of the two methods. The spectral analysis shows unconditional stability of the two sequential methods, which yields the magnitudes of the amplification factor less than unity. We then show numerical examples, which support the a priori stability and convergence estimates.
- Publication Date:
- Research Org.:
- Texas A & M Univ., College Station, TX (United States). Texas A & M Engineering Experiment Station
- Sponsoring Org.:
- USDOE Office of Fossil Energy (FE)
- OSTI Identifier:
- 1845983
- Alternate Identifier(s):
- OSTI ID: 1495604
- Report Number(s):
- DOE-TAMU-FE0028973-12
Journal ID: ISSN 0045-7825
- Grant/Contract Number:
- FE0028973
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Volume: 341; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; Thermoporomechanics; Sequential scheme; Stability analysis; Unconditional stability
Citation Formats
Kim, Jihoon. Unconditionally stable sequential schemes for all-way coupled thermoporomechanics: Undrained-adiabatic and extended fixed-stress splits. United States: N. p., 2018.
Web. doi:10.1016/j.cma.2018.06.030.
Kim, Jihoon. Unconditionally stable sequential schemes for all-way coupled thermoporomechanics: Undrained-adiabatic and extended fixed-stress splits. United States. https://doi.org/10.1016/j.cma.2018.06.030
Kim, Jihoon. Mon .
"Unconditionally stable sequential schemes for all-way coupled thermoporomechanics: Undrained-adiabatic and extended fixed-stress splits". United States. https://doi.org/10.1016/j.cma.2018.06.030. https://www.osti.gov/servlets/purl/1845983.
@article{osti_1845983,
title = {Unconditionally stable sequential schemes for all-way coupled thermoporomechanics: Undrained-adiabatic and extended fixed-stress splits},
author = {Kim, Jihoon},
abstractNote = {In this work, we propose two sequential methods for the all-way coupled thermoporomechanical problems: the undrained-adiabatic split that combines together the undrained and adiabatic methods of poromechanics and thermomechanics, respectively, and the extended fixed-stress split. We perform nonlinear stability analysis for the two sequential methods, introducing a new extended norm that can encompass the all-way coupled thermoporomechanical problems. We find that the two sequential methods are unconditionally stable if α ≥ 0.5, where α is the parameter of time discretization for the generalized midpoint rule at tn+α. We also perform the spectral analysis in order to further investigate stability and convergence of the two methods. The spectral analysis shows unconditional stability of the two sequential methods, which yields the magnitudes of the amplification factor less than unity. We then show numerical examples, which support the a priori stability and convergence estimates.},
doi = {10.1016/j.cma.2018.06.030},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = ,
volume = 341,
place = {United States},
year = {Mon Jun 25 00:00:00 EDT 2018},
month = {Mon Jun 25 00:00:00 EDT 2018}
}
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