I have been largely interested in being able to do small scale simulations with modifications to standard well understood techniques that allow us to gain insights into physical understanding of a system like a galaxy. The method I have most used to this purpose was to ``marry'' one code with another, so as to have the best of both worlds.
Tree-PM: During my thesis I worked on a code that attempted to put to best use the fine resolution of the Barnes & Hut treecode with the speed of a particle-mesh (PM) code. To achieve this I first ran a PM code simulating a region of the Universe that was big enough to include several density peaks of the mass-scale that is of our interest. I visually inspected the resulting block of the Universe at the end of the simulation (z = 0) and pick a small region in the box that contains the density peak that interests us. I then re-ran the PM simulation, this time flagging all the particles that passed through this box. At the end of this run I then have all the particles that are at any time associated with the density peak of our interest. All these particles are then broken up into smaller particles with less mass than the originals. Their positions and velocities is perturbed about the original massive particle by re-realising the (random Gaussian) density field on scales sufficiently fine for the new mass of the particles. These less massive particles are run using the Treecode in high resolution. The more massive particles that were never broken are used to re-run the PM simulation (for the third time). Thus the coarse PM simulation acts as a boundary condition for the tree particles that fall in to the density peak. I can therefore model at the same time infall and tidal torques.
Harmonics-Rings: I've written code simulate disk galaxies using a N-body code, that solves the Poisson equation, by expanding the potential and density in terms of products of Bessel functions, sine and cosine functions and some basis functions in the z direction that fall off suitably fast with increasing z. We use cylindrical coordinates to solve the Poisson equations.
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