Implementation of a Variable Stepsize Variable Formula Method in the TimeIntegration Part of a Code for Treatment of LongRange Transport of Air Pollutants
Abstract
A mathematical model consisting of two partial differential equations is used to study the longrange transport of sulphur dioxide and sulphate over Europe. The discretization of the firstorder space derivatives ( the advection terms) is carried out by a pseudospectral (Fourier) algorithm. A special technique is applied in the discretization of the secondorder space derivatives ( the diffusion terms). Two large systems of ordinary differential equations are solved at each timestep. It is shown that these systems can efficiently be treated by a variable stepsize variable formula method (VSVFM) based on the use of predictorcorrector schemes. The stepsize selection strategy and the formula selection strategy are discussed in detail. An attempt to carry out both an accuracy control and a stability control is made at each timestep. The great efficiency of the VSVFM implemented in our software as well as the reliability of the results are illustrated by numerical experiments, in which real meteorological data (for 1979) at the gridpoints of a space domain covering the whole of Europe were used. The main ideas, implemented in the timeintegration part, might be applied in many other situations, where the systems of ordinary differential equations arising after the space discretization are only moderately stiff (so that the stability requirements are dominant over the accuracy requirements on a large part of the timeinterval but the use of implicit timeintegration algorithms that require solving systems of algebraic equations at each timestep is not justified). As an illustration only it should be mentioned that such an application has been carried out in connection with models describing longrange transport of nitrogen pollutants over Europe.
 Publication:

Journal of Computational Physics
 Pub Date:
 August 1984
 DOI:
 10.1016/00219991(84)90007X
 Bibcode:
 1984JCoPh..55..278Z