Unconditionally stable sequential schemes for all-way coupled thermoporomechanics: Undrained-adiabatic and extended fixed-stress splits

Kim, Jihoon

doi:10.1016/j.cma.2018.06.030

Unconditionally stable sequential schemes for all-way coupled thermoporomechanics: Undrained-adiabatic and extended fixed-stress splits

Journal Article · Mon Jun 25 00:00:00 EDT 2018 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2018.06.030· OSTI ID:1845983

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Texas A & M Univ., College Station, TX (United States); Texas A&M University

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 t_n+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.

View Accepted Manuscript (DOE)

Research Organization:: Texas A & M Univ., College Station, TX (United States). Texas A & M Engineering Experiment Station

Sponsoring Organization:: USDOE; USDOE Office of Fossil Energy (FE)

Grant/Contract Number:: FE0028973

OSTI ID:: 1845983

Alternate ID(s):: OSTI ID: 1614328
OSTI ID: 1495604

Report Number(s):: DOE-TAMU--FE0028973-12

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 341; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
Sequential scheme
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