This page contains pointers to one of my doctoral dissertations, which I delivered in 1995 to the Australian National University's Standing Committee of the Council of the University. While I am not particularly happy with it (but then can anyone be truly happy with their PhD dissertation?), I have put it on the Web, because it contains some interesting stuff that may be of use to other researchers in this area.

And the reviewers liked it too.

The dissertation is split in two volumes available as:

- Volume 1
- spmhd-600dpi.ps.gz, 4.4MB
- The basic formalism
- Verification of the SPH and the weighted differences method
- Coding: vectorization and Connection Machine algorithms
- 3D structure of accretion disks
- Gravitational collapse of a magnetized vortex - a model of the Galactic center
- Comparison with Zeus3D

- Volume 2
- tokamak-600dpi.ps.gz, 819kB
- 3D model of a tokamak based on the Maschke-Perrin solution

I attach excerpts from the reviewers' comments:

- Reviewer 1
- It is my assessment that this thesis represents a significant and carefully executed body of work. Unusual attention has been given to the derivation of the numerical equations and their relations or similarities to other techniques. While others have developed codes based on the SPH technique to simulate megneto-hydrodynamic flows, this work figures among the best documented and tested. This is very important as this numerical method is still somewhat controversial.
- Reviewer 2
- This thesis is a comprehensive and careful study of the accuracy of SPH estimation of gradients and the application of SPH to the simulation of magnetohydrodynamic phenomena. I read it with great interest. In respect of the accuracy of SPH, which occupies the first two chapters, [the author] has made a careful study of aspects of this problem. As he rightly observes, SPH is a technique for working with disordered grids or nodes, and it may be implemented in [various] ways. [...] [Author's] work on MHD problems is a significant contribution to a difficult astrophysical problem. He has tackled this problem very professionally with careful comparison against the Zeus code.
- Reviewer 3
- For the first time [SPH has been] rigorously examined [...]. Merits and limits of the SPH are mathematically and objectively well analysed through the definition of a "figure of merit". Valuable improvement of the SPH is also proposed by an appropriate reformulation of the SPH by utilization of the Weighted Differences Method. [...] Astrophysical phenomena, here studied, are well understood and clearly exposed. Interesting results have been obtained studying the accretion disk structure in binary systems, as the Karman vortex formation. The issue of the magnetised cloud collapse in the galaxy centre is also very well analysed, with many informations on numerical and astrophysical details. Code testing is very accurate, in particular I find the comparison with the Maschke-Perrin solution extremely interesting. Comparison between SPH and Zeus code is very well analysed and discussed.

This dissertation is also mentioned at http://www.icemcfd.com/cfd/sph.html but pointers contained therein are no longer valid (a perennial problem with WWW pages), since they point to a machine, cisr.anu.edu.au, that no longer exists.

Tuesday, 20th of January 2004