Monotone finite-difference approximations to the advection- condensation problem

We discuss herein numerical difficulties with finite-difference approximations to the thermodynamic conservation laws near sharp, cloud-environment interfaces. In order to suppress false oscillations in the solutions, we consider special techniques which derive from the flux-corrected transport (FCT) methodology. 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-steps formulation, we develop an FCT advection scheme which preserves the monotone character of transported thermodynamic variables and also ensures monotonicity of the relative humidity field diagnosed after the advection step. For the conserative variables formulation, we derive a simple and efficient FCT scheme that ensures nonoscillatory thermodynamic fields diagnosed from the advected variables. -from Authors