Application of the Volume-of-Fluid Method to the Advection–Condensation Problem

Abstract

The authors demonstrate the application of the volume of fluid (VOF) method, a specialized grid refinement technique, to the numerical simulation of clouds. In particular, it is shown that VOF eliminates most of the well-recognized numerical difficulties (spurious oscillations and/or diffusion in vicinity of a cloud?environment interface) associated with finite-difference Eulerian advection of cloud boundaries. In essence, VOF is a subgrid-scale advection parameterization that accounts for the transport of material interfaces. VOF is an Eulerian approach, as it does not track explicitly material interfaces. Instead, it reconstructs such interfaces using auxiliary dependent variables?the partial volume fractions of immiscible materials within computational cells. A feature of VOF particularly important for cloud modeling is its ability to identify cells with a subgrid-scale cloud?environment interface. Consequently, relevant parameterizations of microphysical processes can be applied consistently in ?clear? and ?cloudy? regions. In this study, the authors first demonstrate the advantages of VOF using the elementary advection?condensation problem with a known analytic solution. The results of this exercise document that simulations employing VOF are significantly more accurate; to achieve equivalent accuracy, they require almost one order of magnitude less spatial resolution. Next, the method is applied to simulations of both dry and moist thermals. These calculations demonstrate the importance of minimizing numerical diffusion at the cloud?enviroment interface to accurately capture small-scale flow features evolving in the vicinity of the cloud boundary.