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This work discusses the numerical aspects of representing the diffusional(condensational) growth in particulate systems such as atmospheric clouds. Itfocuses on the Eulerian modeling approach, in which the evolution of theparticle size spectrum is carried out using a fixed-bin discretizationassociated with inherent numerical diffusion. Focus is on the applications ofMPDATA numerical schemes (variants explored include: infinite-gauge,non-oscillatory, third-order-terms and recursive antidiffusive correction).Methodology for handling coordinate transformations associated with bothparticle size distribution variable choice and numerical grid layout areexpounded. Analysis of the performance of the scheme is performed using: (i) ananalytically solvable box-model test case, and (ii) the single-column "KiD"test case in which the size-spectral advection due to condensation is solvedsimultaneously with the spatial advection in the vertical physical coordinate,and in which the supersaturation evolution is coupled with the droplet growththrough water mass budget. The single-column problem involves numericalsolution of a two-dimensional advection problem (spectral and spatialdimensions). The box-model simulations demonstrate that, for the problemconsidered, even a tenfold decrease of the spurious numerical spectralbroadening can be obtained by a proper choice of the MPDATA variant(maintaining the same spatial and temporal resolution), yet at an increasedcomputational cost. Analyses using the single-column test case reveal that thewidth of the droplet size spectrum is affected by numerical diffusion pertinentto both spatial and spectral advection. Application of even a single correctiveiteration of MPDATA robustly decreases the relative dispersion of the dropletspectrum, roughly by a factor of two at the levels of maximal liquid watercontent.

On numerical broadening of particle size spectra: a condensational growth study using PyMPDATA