  We present approaches for the study of fluid-structure interactions subject
to thermal fluctuations. A mixed mechanical description is utilized combining
Eulerian and Lagrangian reference frames. We establish general conditions for
operators coupling these descriptions. Stochastic driving fields for the
formalism are derived using principles from statistical mechanics. The
stochastic differential equations of the formalism are found to exhibit
significant stiffness in some physical regimes. To cope with this issue, we
derive reduced stochastic differential equations for several physical regimes.
We also present stochastic numerical methods for each regime to approximate the
fluid-structure dynamics and to generate efficiently the required stochastic
driving fields. To validate the methodology in each regime, we perform analysis
of the invariant probability distribution of the stochastic dynamics of the
fluid-structure formalism. We compare this analysis with results from
statistical mechanics. To further demonstrate the applicability of the
methodology, we perform computational studies for spherical particles having
translational and rotational degrees of freedom. We compare these studies with
results from fluid mechanics. The presented approach provides for
fluid-structure systems a set of rather general computational methods for
treating consistently structure mechanics, hydrodynamic coupling, and thermal
fluctuations.
