Mathematical model for studying the sulphur pollution over Europe

摘要

The long-range transport of sulphur pollutants in the atmosphere is an important environmental problem. A mathematical model, consisting of a system of partial differential equations, has been developed at the Danish Agency of Environmental Protection for studying this phenomenon. The model is handled numerically. A pseudospectral (Fourier) algorithm is used in the space discretization phase. A variable stepsize variable formula method (VSVFM), based on predictor corrector schemes, may be specified during the time-discretization part. The time-integration formulae are especially constructed so that: (a) the predictor-corrector schemes have good absolute stability properties on the imaginary axis and (b) the fundamental properties (consistency, zero-stability and convergence) of the global VSVFM are not affected by the changes of the stepsize and/or the predictor-corrector scheme. Both the accuracy requirements and the stability requirements are taken into account in the stepsize selection strategy as well as in the formula selection strategy. This double check leads to a great efficiency in the numerical treatment of problems arising in atmospheric environments. This is demonstrated by many numerical results. The question of the reliability of the results obtained in runs of real physical problems is discussed. Some results obtained in the comparison of calculated results with measurements are reported. An illustration, where the model is applied in studying the air pollution in the area around Denmark due to Danish sources, is presented.