Atmospheric air quality modeling relies in part on numerical simulation. Required numerical simulations are often hampered by lack of computer capacity and computational speed. This problem is most severe in the field of global modeling where transport and exchange of trace constituents are studied in the whole of the global troposphere/stratosphere. Studies in this field easily lead to computations with millions of unknowns over long time spans. Use of fast, tailored numerical algorithms implemented on the most advanced computer systems is then needed for making real progress. This paper is devoted to a performance study of algorithms developed for solving global atmospheric transport–chemistry problems. The algorithms are applied within two different operator splittings and are vectorized and parallelized on a Cray C90. For the performance study we use a constructed, three-space-dimensional model problem, containing advection, vertical turbulent diffusion and chemical reactions. This numerical model problem is presented as a benchmark on which other algorithms and implementations can be tested. The benchmark problem together with all the algorithm software is available through World Wide Web. In the context of operator splitting, particular attention is paid to the issue of solving chemistry and vertical turbulent diffusion coupled or uncoupled.
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Mathematics and Computers in Simulation
Computational Dynamics

Spee, E., Verwer, J., de Zeeuw, P., Blom, J., & Hundsdorfer, W. (1998). A numerical study for global atmospheric transport-chemistry problems. Mathematics and Computers in Simulation, 48(2), 177–204.