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Published October 1997 | public
Journal Article

Benchmarking stiff ode solvers for atmospheric chemistry problems-I. implicit vs explicit


In many applications of atmospheric transport-chemistry problems, a major task is the numerical integration of the stiff systems of ordinary differential equations describing the chemical transformations. This paper presents a comprehensive numerical comparison between five dedicated explicit and four implicit solvers for a set of seven benchmark problems from actual applications. The implicit solvers use sparse matrix techniques to economize on the numerical linear algebra overhead. As a result they are often more efficient than the dedicated explicit ones, particularly when approximately two or more figures of accuracy are required. In most test cases, sparse RODAs, a Rosenbrock solver, came out as most competitive in the 1% error region. Of the dedicated explicit solvers, TWOSTEP came out as best. When less than 1% accuracy is aimed at, this solver performs very efficiently for tropospheric gas-phase problems. However, like all other dedicated explicit solvers, it cannot efficiently deal with gas-liquid phase chemistry. The results presented may constitute a guide for atmospheric modelers to select a suitable integrator based on the type and dimension of their chemical mechanism and on the desired level of accuracy. Furthermore, we would like to consider this paper an open invitation for other groups to add new representative test problems to those described here and to benchmark their numerical algorithms in our standard computational environment.

Additional Information

The work of the authors Sandu, Carmichael and Potra was supported in part by the DOE under grant no DE-FG02-94ER 61855 and by the Center for Global and Regional Environmental Research. The authors Verwer and Van Loon gratefully acknowledge support from the RIVM (Dutch National Institute of Public Health and Environmental Protection) for the projects EUSMOG and CIRK.

Additional details

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October 25, 2023