Development and analysis of a non-splitting solution for three-dimensional air quality models

This paper examines the errors introduced by operator splitting techniques in air quality models. Results are presented for different time steps used in the splitting schemes as well as for different ordering in which the operators are computed. Furthermore, a non-splitting technique is developed to analyze the performance of operator splitting techniques in air quality models. Convergence rates of operator splitting schemes are determined. Research indicates splitting techniques provides at most linear convergence. For fast-reacting species like N2O5; the convergence is not achieved when using splitting methods and time steps as small as 10 s: Symmetric and non-symmetric operator splitting does not provide significant difference in accuracy. Furthermore, operator splitting ordering with stiff operators computed last does not produce better results than with non-stiff operators computed last. The non-splitting method developed achieves convergence by reducing time steps, adapting time steps to insure convergence, and eliminating operator splitting. r 2003 Elsevier Ltd. All rights reserved.