Monotone Finite-Difference Approximations to the Advection-Condensation Problem

Abstract

Abstract We discuss herein numerical difficulties with finite-difference approximations to the thermodynamic conservation laws near sharp, cloud-environment interfaces. The Conservation laws for entropy and water substance variables are coupled through the phase change processes. This coupling of the thermodynamic equations may lead to spurious numerical oscillations that, in general, are not prevented by direct application of traditional monotone methods developed for the uncoupled equations. In order to suppress false oscillations in the solutions, we consider special techniques which derive from the flux-corrected-transport (FCT) methodology. In these, we incorporate physical information about condensation-evaporation processes directly into the limiters constraining the antidiffusive fluxes of the FCT methods. We elaborate upon two different advection-condensation schemes relevant to the two formulations of the advection-condensation problem, commonly used in cloud modeling. For the fractional-time-st...