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

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.