Numerical schemes to model condensation and evaporation of aerosols

A positive-definite scheme is developed to solve the aerosol condensation and evaporation problem. Bott's positive-definite advection scheme (Bott, 1989a) is used to model the movement of the distribution in the size coordinate while analytical solutions are derived to model the growth term. The numerical predictions of the positive-definite scheme are compared with that of previous attempts to model this equation, i.e. a finite-element-finite-difference method and accurate space derivatives scheme (ASD). New analytical solutions are derived for the condensation/evaporation equation and these are used to estimate the accuracy of the schemes for modeling single component and multicomponent cases. The scheme is seen to be accurate at small Courant numbers and is numerically very efficient.