  In molecular simulation and fluid mechanics, the coupling of a particle
domain with a continuum representation of its embedding environment is an
ongoing challenge. In this work, we show a novel approach where the latest
version of the adaptive resolution scheme (AdResS), with non-interacting
tracers as particles reservoir, is combined with a fluctuating hydrodynamics
(FHD) solver. The resulting algorithm, supported by a solid mathematical model,
allows for a physically consistent exchange of matter and energy between the
particle domain and its fluctuating continuum reservoir. Numerical tests are
performed to show the validity of the algorithm. Differently from previous
algorithms of the same kind, the current approach allows for simulations where,
in addition to density fluctuations, also thermal fluctuations can be accounted
for, thus large complex molecular systems, as for example hydrated biological
membranes in a thermal field, can now be efficiently treated.
