Numerical time integration for air pollution models

Due to the large number of chemical species and the three space dimensions, off-the-shelf stiff ODE integrators are not feasible for the numerical time integration of stiff systems of advection-diffusion-reaction equations [ fracpar{c{t + nabla cdot left( vu{u c right) = nabla cdot left( K ,nabla, c right) + R left( c right), c=c(vu{x,t), c in IR^m, vu{x in Omega subset IR^3 ] 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 will 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 CWI over approximately the last 5 years.