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
