Numerical solution of the aerosol condensation/evaporation equation

A new method is developed to solve the condensation equation as it relates to Air Quality Models using both semi-Lagrangian and Lagrangian fluxes to increase resolution and perform accurately under stringent conditions that occur in the atmosphere. The new method, Partitioned Flux Integrated Semi-Lagrangian Method (PFISLM), can be used with lower-order interpolators and they produce highly accurate results. PFISLM is positive definite, peak retentive, mass conservative, and suppresses oscillations. Research indicates the differences between PFISLM and other traditional flux integrated semi-Lagrangian methods are significant when solving the aerosol condensation/evaporation equation. PFISLM is created to handle specific difficulties associated with the time and space discretization of the aerosol operator in air quality models.