Semi-lagrangian flux scheme for the 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 produces highly accurate results. PFISLM is positive definite, peak retentive, mass conservative, and suppresses oscillations. Research indicates that the differences between PFISLM and traditional flux integrated semi-Lagrangian methods as proposed by Bott (1989) and Emde (1991) 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.