  We present a computation of NNLO QCD corrections to the production of a Higgs
boson in association with a $W$ boson at the LHC followed by the decay of the
Higgs boson to a $b\bar{b}$ pair. At variance with previous NNLO QCD studies of
the same process, we treat $b$ quarks as massive. An important advantage of
working with massive $b$ quarks is that it makes the use of flavor jet
algorithms unnecessary and allows us to employ conventional jet algorithms to
define $b$ jets. We compare NNLO QCD descriptions of the associated
$WH(b\bar{b})$ production with massive and massless $b$ quarks and also
contrast them with the results provided by parton showers. We find ${\cal
O}(5\%)$ differences in fiducial cross sections computed with massless and
massive $b$ quarks. We also observe that much larger differences between
massless and massive results, as well as between fixed-order and parton-shower
results, can arise in selected kinematic distributions.
