  In this paper, the inherent gradient flow structures of
thermo-poro-visco-elastic processes in porous media are examined for the first
time. In the first part, a modelling framework is introduced aiming for
describing such processes as generalized gradient flows requiring choices of
physical states, corresponding energies, dissipation potentials and external
work rates. It is demonstrated that various existing models can be in fact
written within this framework. Ultimately, the particular structure allows for
a unified well-posedness analysis performed for different classes of linear and
non-linear models. In the second part, the gradient flow structures are
utilized for constructing efficient discrete approximation schemes for
thermo-poro-visco-elasticity -- in particular robust, physical splitting
schemes. Applying alternating minimization to naturally arising minimization
formulations of (semi-)discrete models is proposed. For such, the energy
decrease per iteration is quantified by applying abstract convergence theory
only utilizing convexity and Lipschitz continuity properties of the problem --
a fairly simple but flexible machinery. By this approach, e.g., the widely used
undrained and fixed-stress splits for the linear Biot equations are derived and
analyzed. By application of the framework to more advanced models, novel
splitting schemes with guaranteed theoretical convergence rates are naturally
derived. Moreover, based on the minimization character of the (semi-)discrete
equations, relaxation of splitting schemes by line search is proposed;
numerical results show a potentially great impact on the acceleration of
splitting schemes for both linear and nonlinear problems.
