  We investigate the free convection processes in the vicinity of a spherical 1
kg mass standard by two- and three-dimensional direct numerical simulations
using a spectral element method. Our focus is on the determination and
suppression of updraft forces in a high-precision mass comparator which are
caused by temperature differences between mass standard and its environment in
the millikelvin range - a source of systematic uncertainties in the
high-precison mass determination. A two-dimensional model is presented first,
which obtains a good agreement with previous laboratory measurements for the
smaller temperature differences up to 15 mK. The influence of different
boundary conditions and side lengths of the square domain is discussed for the
mass standard positioned in the center of the chamber. The complexity is
increased subsequently in configurations with additional built-ins for counter
heating in form of planar plates or hemispherical shells above the mass
standard. The latter ones lead to a full compensation of the updraft force.
Three-dimensional simulations in a closed cubic chamber confirm the
two-dimensional findings and additionally reveal complex secondary flow pattern
in the vicinity of the mass standard. The reduction of the heat transfer due to
the built-ins is also demonstrated by a comparison of the Nusselt numbers as a
function of the Rayleigh number in the chosen parameter range. Our simulations
suggest that such additional constructive measures can enhance the precision of
the mass determination by suppression of free convection and related systematic
uncertainties.
