Unconditionally stable sequential schemes for thermoporomechanics: Undrained-adiabatic and extended fixed-stress splits
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Copyright 2015, Society of Petroleum Engineers. We study unconditionally stable sequential methods for the all-way coupled thermoporomechanical problems. We first propose two sequential methods: The undrained-adiabatic split that combines the undrained split in poromechanics with the adiabatic split in thermomechanics, and the extended fixed- stress split. We perform new stability and convergence analysis for the undrained-adiabatic and extended fixed-stress split methods, introducing a new extended norm for nonlinear stability analysis, which can cover all-way coupled thermoporomechanical problems. In this study we show that the two methods are unconditionally stable (i.e., contractive and B-stable), when we take implicit time stepping. We also perform spectral analysis in order to investigate convergence of the two methods when linearizing the coupled problem. The spectral analysis will be useful for designing reliable pre-conditioners of the monolithic method. The spectral analysis shows that the two sequential methods are convergent and that the extended-fixed stress split is more accurate than the undrained-adiabatic split for strong coupling. We show numerical examples, which support the a-priori stability and convergence estimates.
