The following is about a collaboration which lasted for 3 years and finally resulted in a publication by Horst Fichtner, Han de Bruijn (= myself) and S. Ranga Sreenivasan. The paper is titled: Longitudinal gradients of the distribution of anomalous cosmic rays in the outer heliosphere

How comes that someone who is working at the former Computing Centre of a Technical University is going to collaborate with an astronomer? Well, that's bit of a strange story indeed!

I have decided to distribute the computer programs and accompanying documentation, with exception of the "coeffs" suroutine (containing all of the Physics and developed by Horst Fichtner himself), as public domain source code. It might serve as a (somewhat obsoleted) blueprint for describing anisotropic Convection & Diffusion within a hemisphere. The mathematics of Convection & Diffusion should better be replaced by a proper translation from my newer Delphi Pascal version. Also available are LaTeX sources of the accompanying MathJax document, with a somewhat obsolete description of Convection. [ Note. Modern insights are worded here but they are not implemented (yet) in the ZONWIND code. ] Anyway, here are some visualizations of results obtained by Horst Fichtner.

I was in the opportunity to present a lecture about the numerics of the matter at the "Woudschoten 1996 conference" on September 26th, Thursday, 12.15 - 12.45, Zeist (the Netherlands). Title of the presentation: "On solving a Cosmic Ray equation". A (necessarely incomplete: partly hand-written) collection of accompanying overhead sheets was processed for inclusion in this Homepage.

I've been successful in porting a full blown version of the 3-D ZONWIND code to PC's, using (Turbo Pascal and) Delphi.

Delphi Pascal

The units where the calculations are done are also available as a Visual (Delphi) Pascal source code. Due to Delphi's nature, it's difficult to publish every single detail, though. Naming conventions are a clear reference to earlier developments.
Larger versions of the program use more than 35 MB of memory (hence 64 MB is recommended) and quite a bit of CPU power. Features:
  1. Hemisphere or Whole Sphere as the integration domain
  2. Comparison with analytical solutions of the Cosmic Ray problem
    as well as real world coefficients
  3. Elements for (Anisotropic) Convection and Diffusion
  4. Iterative Methods for solving the Equations:
    • Incremental Successive Overrelaxation
    • Incremental Jacobi with Preconditioning
  5. Last but not least: the executable as a whole
For an excellent description of Iterative Methods for Large Sparse Systems of Equations
unzip and print the Templates PS document (mirrorred from netlib).
The "Incremental Jacobi with Preconditioning" method was discovered only after some weird and seemingly fruitless research.
(Warning: neither does it converge under all circumstances!)