  In this work we are interested in effectively solving the quasi-static,
linear Biot model for poromechanics. We consider the fixed-stress splitting
scheme, which is a popular method for iteratively solving Biot's equations. It
is well-known that the convergence of the method is strongly dependent on the
applied stabilization/tuning parameter. In this work, we propose a new approach
to optimize this parameter. We show theoretically that it depends also on the
fluid flow properties and not only on the mechanics properties and the coupling
coefficient. The type of analysis presented in this paper is not restricted to
a particular spatial discretization. We only require it to be inf-sup stable.
The convergence proof applies also to low-compressible or incompressible fluids
and low-permeable porous media. Illustrative numerical examples, including
random initial data, random boundary conditions or random source terms and a
well-known benchmark problem, i.e. Mandel's problem are performed. The results
are in good agreement with the theoretical findings. Furthermore, we show
numerically that there is a connection between the inf-sup stability of
discretizations and the performance of the fixed-stress splitting scheme.
