Numerical Algorithms for Transport-Chemistry Problems

At CWI new numerical techniques are developed and used in the study of the transport of pollutants. More in particular the studies concentrate on three applications: transport simulation of pollutants and sediments in shallow seas, transport simulation of trace constituents in the global troposphere, and smog prediction.

Negative effects of emission of pollutants in the atmosphere, groundwater and surface water become more and more noticeable in our environment: smog in urban regions, ground water contamination, the growth of algae in surface water, and even atmospheric climate change has to be feared. In the study of the long term effects of these emissions and in the prediction of the efficiency of policy decisions to reduce the effects mathematical simulations become increasingly important. The processes are described by a large system of coupled time dependent three-dimensional partial differential equations of the advection-diffusion-reaction type, one for each chemical species that plays a role in the reactive chain. Computer capacity is a critical factor here, and although computer power continues to expand, the computational requirements for high resolution transport models with full chemistry are still out of range for many applications.

Numerical analysis can help to find more efficient simulation tools and to fully exploit emerging computer architectures such as advanced multi-vector processors and massively parallel processing systems. In realistic environmental models the number of species can be large, for example up to 100 in current atmospheric models. Also the spatial domain can be large, requiring hundred thousands to millions of grid points. Moreover, in order to study long term effects, the equations have to be integrated over long time intervals. Such models require an excessive amount of CPU and memory which necessitates fast and efficient algorithms, even on modern supercomputers. This poses a number of outstanding numerical challenges.

Computational grid at ground level at the end of a 5-day prediction of SO2 concentrations

CWI has contributed in several ways to the solution of these problems.

• Atmospheric chemical reactions usually take place on very different time scales. The implicit methods used to deal with such `stiff' problems require a lot of computer storage. An alternative has been developed employing a Gauss-Seidel iteration, which combines the advantages of explicit (fast) and implicit (stable) methods.
• For an atmospheric benchmark problemt was shown that chemistry and vertical diffusion can be solved simultaneously in an efficient way, keeping `splitting errors' within limits.
• For an explicit solution of advective transport in shallow water, numerical stability will in general require very small time steps and hence reduce efficiency. Several ways to avoid small time steps have been examined, including Hopscotch type splitting and dimension splitting.
• Local grid refinements are examined in connection with regional air-pollution models developed for smog prediction.
• In a pilot project the possibilities of the CRAY T3D massively parallel system for use in regional atmospheric models are considered.

The research at CWI is carried out in three projects:

• In EUSMOG - a collaborative project with the Dutch National Institute of Public Health and Environmental Protection - fast numerical algorithms are developed for the prediction of smog episodes. The model uses a 4-layer parameterization in the vertical direction and a chemical ozone model with 15 species.
• In the TRUST project we study - in collaboration with Delft University of Technology, the National Institute for Coastal and Marine Management, Delft Hydraulics, and other partners participating in the EU MAST II project NOWESP - the simulation of transport and bio-chemical interaction of salinity, pollutants, suspended material, etc., in shallow seas, such as the North Sea. CWI research focuses on fast, parallel algorithms for the time integration of the advection-diffusion- reaction equations.
• CIRK is a joint project with the Institute for Marine and Atmospheric Research of Utrecht University, the Dutch National Institute of Public Health and Environmental Protection, and the Royal Netherlands Meteorological Institute. The goal is to develop an improved model for global transport and chemistry of trace constituents in the troposphere. CWI studies numerical aspects of advection on spherical geometries, fast chemical solvers, computational aspects of operator splitting, and vectorization and parallelization aspects.

Please contact:
Jan Verwer - CWI
Tel: +31 20 592 4095
E-mail: janvcwi.nl

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