  This work discusses the numerical aspects of representing the diffusional
(condensational) growth in particulate systems such as atmospheric clouds. It
focuses on the Eulerian modeling approach, in which the evolution of the
particle size spectrum is carried out using a fixed-bin discretization
associated with inherent numerical diffusion. Focus is on the applications of
MPDATA numerical schemes (variants explored include: infinite-gauge,
non-oscillatory, third-order-terms and recursive antidiffusive correction).
Methodology for handling coordinate transformations associated with both
particle size distribution variable choice and numerical grid layout are
expounded. Analysis of the performance of the scheme is performed using: (i) an
analytically solvable box-model test case, and (ii) the single-column "KiD"
test case in which the size-spectral advection due to condensation is solved
simultaneously with the spatial advection in the vertical physical coordinate,
and in which the supersaturation evolution is coupled with the droplet growth
through water mass budget. The single-column problem involves numerical
solution of a two-dimensional advection problem (spectral and spatial
dimensions). The box-model simulations demonstrate that, for the problem
considered, even a tenfold decrease of the spurious numerical spectral
broadening can be obtained by a proper choice of the MPDATA variant
(maintaining the same spatial and temporal resolution), yet at an increased
computational cost. Analyses using the single-column test case reveal that the
width of the droplet size spectrum is affected by numerical diffusion pertinent
to both spatial and spectral advection. Application of even a single corrective
iteration of MPDATA robustly decreases the relative dispersion of the droplet
spectrum, roughly by a factor of two at the levels of maximal liquid water
content.
