×

zbMATH — the first resource for mathematics

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.

MSC:
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
PDF BibTeX XML Cite