Comparison of numerical techniques for use in air pollution models with non-linear chemical reactions

Abstract

The coupled, non-linear system of continuity equations describing an air pollution model with non-linear chemistry is solved numerically using finite differences, finite elements and pseudo-spectral methods. A smoothing procedure is proposed to avoid negative concentrations. Several tests are performed: single puff transported parallel and not parallel to the co-ordinate axis, two puffs along parallel lines, a rotating puff and a rotating plume. The accuracy of the results of advection + chemistry + smoothing calculations is evaluated through the comparison with the results of box model calculations. The concentration at the peak of the puff is compared in the case with advection only, chemistry only and advection + chemistry after 24 h integration. If the advection is performed by a pseudospectral algorithm, then the relative errors made in the case where advection + smoothing + chemistry is applied do not exceed 5%. These errors are of the same magnitude as the errors at the peak of the puff for the case where advection only is performed. For runs with discretization by second order finite differences, it is well known that the advection algorithms are neither able to preserve the shape of the puff nor to preserve the maximum concentrations in the puff. Our runs only confirmed this conclusion. For runs with the Smolarkiewicz algorithm, the results are slightly better than with the algorithm based on second order finite differences. However, the improvement of the accuracy is negligible compared with the increase of the computing time spent. The runs with the finite elements (CHAPEAU) advection algorithm show that the accuracy of this advection algorithm is worse than that of the pseudospectral advection, but it is faster than the latter algorithm with regard to computing time. The second order finite differences algorithm is about 5 times faster than the pseudospectral algorithm when the advection time only is taken into account. In the same situation the Smolarkiewicz algorithm is only a little better than the pseudospectral algorithm, while the finite elements (CHAPEAU) algorithm is about 2.S times faster. The differences are less when advection + smoothing + chemistry is applied.