Modelling numerically any astrophysical phenomena in general has proven challenging, even taking into consideration some considerable simplifications. However with the improvements in computing from the late nineties onwards reasonable 3-dimensional approximations of galactic features have been developed.
The aim of this section of the chapter is to briefly review progress and to summarise some key findings to date. To impose some finite limit on the scope of the review we restrict our attention to three dimensional models, which include realistic parameters on galactic scales. Please attribute any omissions as a reflection of the ignorance of this author and not on the value of the work.
We present a roughly chronological review of models and their methods, objectives and results. This approach evolves out of the earlier 2D study by Rosen et al. (1993) which investigated the hydrodynamical turbulent structure of the ISM using stellar heating and star formation.
Tomisaka (1998) attempted to model multiple supernovae (SNe) in 3D using a super-bubble approximation of in a stratified ISM with magnetic field. We summarise in Table 1 some key features of the models, which followed subsequently.
| Korpi (a) | Avillez (b) | Hanasz (f) | Balsara (c) | Slyz (d) | Piontek (d) | Joung (b) | Gressel (e) | |
| Domain, kpc | 0.5 × 0.5 × 2 | 1 × 1 × 5-20 | 0.5 × 1 × 1.2 | 0.23 | 1.283 | 0.23 | 1 × 1 × 10 | 0.5 × 0.5 × 4 |
| Res, pc | 8 | 1.25-10 | 10-100 | 0.78-1.56 | 10-20 | 0.78-1.56 | 1.95 | 2-8 |
| Heating | SN II+SN I | SN II+SN I | CR | SN | SN | - | SN II+SN I | SN II+SN I |
| Temp, K | 102-108 | 2 × 102-106 | 2 × 102-106 | 102-108 | 102-108 | 101.5-m104 | 2 × 102-107 | 1-107 |
| Phases | warm(W)+hot(H) | cold(C)+W+H | C+W+H | W+H | C+W+H | C+W | C+W+H | C+W+H |
| MHD | non-ideal | hydro & ideal | non-ideal | ideal | hydro | ideal | hydro | non-ideal |
| Diffusion | hyper 
 |
- | |
- | - | |
- |
|
| Gravity | stellar+halo | stellar+halo | stellar+halo | - | self gravity | linear z | stellar+halo | yes |
| Rotation | differential | - | rigid & differential | - | - | differential | - | differential |
| Cosmic rays | - | - | yes | - | - | - | - | - |
| Star forming | - | - | - | - | yes | - | - | - |
| Duration | 100 Myr | 400 Myr | 4.8 Gyr | - | 350 Myr | 2 Gyr | 80 Myr | 1 Gyr |
| A summary of three dimensional simulated models of galaxy features by: Korpi et al. (1999)(a), de Avillez and Breitschwerdt (2007)(b) from 2000, Hanasz et al. (2009)(c) from 2004, Balsara et al. (2004)(d), Slyz et al. (2005)(e), Piontek and Ostriker (2007)(f) from 2005, Gressel et al. (2008)(f). | ||||||||