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Numerical time integration for air pollution models. (English) Zbl 0999.65097
Summary: Due to the large number of chemical species and the three space dimensions, off-the-shelf stiff ordinary-differential-equation integrators are not feasible for the numerical time integration of stiff systems of advection-diffusion-reaction equations from the field of air pollution modelling. This has led to the use of special time integration techniques This paper is devoted to a survey of such techniques, encompassing stiff chemistry solvers, positive advection schemes, time or operator splitting, implicit-explicit methods, and approximate matrix factorization solutions. Of great importance in practice is high-performance computing due to the huge problem scales, in particular for global models.
We therefore also report on experiences with vector/parallel shared memory and massively parallel distributed-memory architectures and clusters of workstations. The survey is not entirely unique to air pollution models and biased towards work done at the Centrum voor Wiskunde en Informatica, Amsterdam.

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L05 Numerical methods for initial value problems involving ordinary differential equations
65Y20 Complexity and performance of numerical algorithms
80A32 Chemically reacting flows
35K57 Reaction-diffusion equations
65Y05 Parallel numerical computation
92D40 Ecology