APPLICATION OF THE VOLUME-OF-FLUID METHOD TO THE ADVECTION-CONDENSATION PROBLEM

The authors demonstrate the application of the volume of fluid (VOF) m ethod, a specialized grid refinement technique, to the numerical simul ation of clouds. In particular, it is shown that VOF eliminates most o f the well-recognized numerical difficulties (spurious oscillations an d/or diffusion in vicinity of a cloud-environment interface) associate d with finite-difference Eulerian advection of cloud boundaries. In es sence, 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 rec onstructs such interfaces using auxiliary dependent variables-the part ial volume fractions of immiscible materials within computational cell s. A feature of VOF particularly important for cloud modeling is its a bility to identify cells with a subgrid-scale cloud-environment interf ace. Consequently, relevant parameterizations of microphysical process es 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 s olution. The results of this exercise document that simulations employ ing VOF are significantly more accurate; to achieve equivalent accurac y, they require almost one order of magnitude less spatial resolution. Next, the method is applied to simulations of both dry and moist ther mals. These calculations demonstrate the importance of minimizing nume rical diffusion at the cloud-enviroment interface to accurately captur e small-scale how features evolving in the vicinity of the cloud bound ary.