Study of Numerical Diffusion in a Discrete-Sectional Model and Its Application to Aerosol Dynamics Simulation

ABSTRACT

The discrete-sectional model is an important tool used to study aerosol dynamics, although it suffers inherent numerical diffusion errors that are dependent on the model parameters including section spacing, numerically conserved aerosol property, and number of discrete sizes. An analytical evaluation of the errors due to the deviations of the derived aerosol properties in the sectional formulation and the interchange between discrete-size and sectional aerosols is carried out. The errors are larger if the difference in the aerosol property function index (ξ) between the derived and conserved properties is larger. Results of parametric studies are reported for condensation and coagulation systems. The results for condensation systems show that the υ-model is better than the n-model and the υ²-model in predicting the integral properties of the size distribution. However, the deviation in the results between the n-model, υ-model, and υ²-model reduces as the section spacing is decreased. A finite value of the geometric standard deviation (σ_g) is obtained for a specific section spacing and is independent of the chosen conserved aerosol property. The results for coagulation systems also show that the υ-model is better in predicting N, V, and υ_g, although the υ²-model is better in predicting the second volume moment, V2, and σ_g. The inclusion of a larger number of discrete sizes gives more precise description of aerosol dynamics for the molecular clusters, although the effect is rather insignificant for the number greater than 20. It is also found that the discrete formulation possesses numerical diffusion in simulating a condensation process.