Abstract
The work discusses the diffusional growth in particulate systems such as atmospheric clouds. It focuses on the Eulerian modeling approach in which the evolution of the probability density function describing the particle size spectrum is carried out using a fixed-bin discretization. The numerical diffusion problem inherent to the employment of the fixed-bin discretization is scrutinized. The work focuses on the applications of MPDATA family of numerical schemes. Several MPDATA variants are explored including: infinite-gauge, non-oscillatory, third-order-terms and recursive antidiffusive correction (double pass donor cell, DPDC) options. Methodology for handling coordinate transformations associated with both particle size distribution variable choice and numerical grid layout are expounded. The study uses PyMPDATA – a new open-source Python implementation of MPDATA. Analysis of the performance of the scheme for different discretization parameters and different settings of the algorithm is performed using an analytically solvable test case pertinent to condensational growth of cloud droplets. The analysis covers spatial and temporal convergence, computational cost, conservativeness and quantification of the numerical broadening of the particle size spectrum. Presented results 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).
Highlights
1.1 Motivation and outlineThe focus of this paper is on the problem of predicting the particle size evolution for a population of droplets undergoing diffusional growth
It focuses on the Eulerian modeling approach in which the evolution of the probability density function describing the particle size spectrum is carried out using a fixed-bin discretization
25 The term spectral broadening refers to the increasing width of the droplet spectrum during the lifetime of a cloud, which may be associated with both physical mechanisms as well as spurious artifacts stemming from the employed numerical solution technique
Summary
The focus of this paper is on the problem of predicting the particle size evolution for a population of droplets undergoing diffusional growth. This work highlights the importance of MPDATA algorithm variant choice for the resultant spectral broadening of the particle size spectrum. The discretization strategies employed in representing the particle size spectrum and its evolution are characterized by inherent limitations which constrains the fidelity of spectral width predictions (e.g., Arabas and Pawlowska, 2011; Morrison et al, 2018). It is presented with the aim of gathering information that is scattered across works focusing on more complex 45 computational fluid dynamics applications of MPDATA. Example simulations employing an analytically solvable test case pertaining to the evolution of cloud droplet size spectrum in a cumulus cloud is used to depict the effects on numerical broadening from enabling the discussed algorithm variants. Appendix A contains convergence analysis based on results of multiple simulations using the embraced test case run with 55 different temporal and spatial resolutions
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