THEMATIC PROGRAMS

October 23, 2014

Numerical and Computational Challenges in Science and Engineering Program

Short Course on "Numerical and Computational Challenges in Environmental Modelling"

Instructor: Zahari Zlatev
National Environmental Research Institute (Denmark)

Schedule: February 5, 7, 12, 14, 19, 2002, 2:00 pm - 4:30 pm

Short description:

The problems connected with the environmental pollution are becoming more and more important. It is necessary to use advanced mathematical models in order to give adequate answers to the numerous questions arising in this field. These models are described by systems of partial differential equations (PDEs). The number of equations is equal to the number of chemical species involved in the model. In the attempts to obtain more reliable results one tries (i) to incorporate more chemical species in the model and/or (ii) to use finer grids in the discretization of the spatial derivatives. This leads to very large computational task. Furthermore, long sequences of scenarios are, as a rule, needed in most of the environmental studies. This is why many challenging problems are to be resolved in order to prepare reliable answers to the asked questions. The solution of some of the problems when systems of PDEs arising in environmental models are handled on modern high-speed computers will be the major topic of this course. Several applications of the models, including the impact of future climate changes (the green house effects) on pollution levels, will also be described. Finally, a series of problems, which are still open, will be presented and discussed.


Most of the problems treated in this course are also discussed in: Zahari Zlatev: "Computer Treatment of Large Air Pollution Models", Kluwer Academic Publishers, Dordrecht-Boston-London, 1995. However, some new results will be presented (copies of relevant materials will be made available as postscript and pdf files).

Contents of lectures:

  1. General discussion of the systems of PDEs arising in environmental models and justification of the need of high-speed computers.
    Lecture Slides

  2. Use of splitting techniques in the numerical treatment of the models.
    Lecture Slides

  3. Treatment of the advection (the horizontal transport) part in an environmental model.
    Lecture Slides

  4. Treatment of the chemical part: general ideas and major numerical methods used in this sub-model.
    Lecture Slides

  5. Partitioning of the ODE system describing the chemical reactions in the model.
    Lecture Slides

  6. Optimizing the matrix computations (types of matrices arising in the treatment of the different parts of an environmental model).
    Lecture Slides

  7. Parallel computations: need for parallel computations and major requirements (standard tools + portability). Use of templates.
    Lecture Slides

  8. Discussion of some typical applications related to different environmental studies.
    Lecture Slides

  9. Impact of future climate changes on high pollution levels.
    Lecture Slides

  10. Open problems and plans for future research efforts.
    Lecture Slides