Eulerian and modified Lagrangian approaches to multi-dimensional condensation and collection

TL;DR

This study compares Eulerian and Lagrangian numerical schemes for modeling cloud droplet growth due to turbulence and gravity, highlighting the advantages of Lagrangian methods and the importance of interpolation schemes.

Contribution

It provides a detailed comparison of Eulerian and Lagrangian approaches for simulating multi-dimensional condensation and collection in clouds, emphasizing computational efficiency and accuracy.

Findings

Lagrangian schemes outperform Eulerian in computational efficiency.

Size spectra tails are well described by a gamma distribution.

Interpolation schemes can negatively impact superparticle approach accuracy.

Abstract

Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here, an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or su- perdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow, or just gravitational acceleration without gas flow. Good agreement between the differ- ent schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. Higher moments of the size spectra are found to be a useful tool to characterize the growth of the largest drops through collection. Remarkably, the tails of the size spectra are reasonably well described by a gamma distribution in cases with gravity or turbulence. The Lagrangian schemes are generally found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results.