ERCIM News No.34 - July 1998

## Numerical Algorithms for Air and Surface Water Quality Modelling

by Jan Verwer

Many environmental problems, such as damage to the biosphere, local air pollution, the spread of harmful substances in the water, and global climatic changes can not be studied by experimentation. Hence, mathematical models and computer simulations are being used as the appropriate means to get more insight. CWI has been active in this field from the early 1990s and co-operates with several organizations within and outside The Netherlands. Significant parts of the research are carried out within the TASC project (Transport Applications and Scientific Computing) and are supported by the national HPCN programme and the Cray University Research Grants Programme.The mathematical models consist of a set of partial differential equations (PDEs) describing the system's evolution in time. By discretizing the time and space variables occurring in the PDEs on a grid, a numerical model is obtained, which is then solved on a computer. Due to the rapid progress in high performance computing this numerical approach is nowadays many times cheaper than building traditional scale models. In addition, many processes such as the spread of pollutants defy accurate simulation by means of scale models.

Solving such realistic time-dependent PDEs numerically is very computation-intensive. Discretization in space coordinates produces a formidable set of ordinary differential equations (ODEs) in which only time occurs as a continuous variable. This set of equations is then solved step-wise in time by means of a numerical integration formula. The choice of the spatial discretization and the integration formula depends on the stability of the evolution process, the desired accuracy of the approximation and the efficiency of the entire computation process.

CWI carries out research jointly with the national Organization for Applied Research TNO to develop a regional 3D long-term ozone simulation model, replacing the current LOTOS model used by TNO. CWI contributes with the design of the mathematical model for a hybrid (terrain following and pressure based) coordinate system and, in particular, of tailored numerical algorithms and implementations on parallel and super-computers.

In a similar project, CIRK, CWI has developed numerical algorithms for use in 3D models describing global changes in the troposphere's chemical composition due to the long-term spread of air polluting substances, taking into account exchange with the stratosphere. The work included stiff chemistry integration and a factorization approach within the Rosenbrock method, as well as the validation of various advection schemes in a real-life radon experiment, using analyzed wind fields from ECMWF. New work in this field centres around the existing TM3 model. Other recently started research in air quality modelling concerns application of operator splitting and sparse-grid methods to advection-diffusion-reaction problems.

CWI's present contributions to water quality modelling are based on a previously developed efficient computing model for 3D shallow-water equations (SWEM). Here a parallel vectorized flow model was implemented on a Cray supercomputer. In SWEM a transport model is coupled to a hydrodynamic model which generates the velocity field for the transport model. Starting from the SWEM model CWI designs parallel numerical methods for the simulation of water pollution (calamitous releases), the marine eco-system, dispersion of river water, sediment transport, etc. In connection with this a 3D transport model was studied, in particular the iterative solution of the equations resulting from their implicit time-discretization, and domain decomposition with domains of varying grid resolutions. Part of the research is carried out in the EU programme MAST within the MMARIE project (Modelling of Marine Eco Systems), with applications to pollution on the Continental Shelf caused by sediment transport from the Rhine and other major European rivers.

For more information see:

- http://dbs.cwi.nl/cwwwi/owa/cwwwi.print_projects?ID=2 (air)
- http://dbs.cwi.nl/cwwwi/owa/cwwwi.print_projects?ID=4 (water)

Please contact:

Jan Verwer - CWI

Tel: +31 20 592 4095

E-mail: Jan.Verwer@cwi.nl

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