For simulations that deal only with collisionless dark matter or stellarsystems, the conventional N-body technique is fast, memory efficient, and relatively simple to implement. It involves directly summing up the individual contributions to gravity from every other particle in a simulation in order to determine the total net gravitational force.

However when including the effects of gas physics, there exist two main types of code. Mesh based codes which model the collisional gas on a mesh, and Smooth Particle Hydrodynamics (SPH) which splits the fluid up into a series of particles of a fixed mass which move with the fluid flow. Implementing the N-body approach into SPH codes is fairly trivial as the gas and collisionless stars and dark matter are all represented as particles. However the particle-mesh technique used in mesh codes requires the particle masses of stars and dark matter to be first mapped to the mesh in order to determine the overall gravitational field which can then be mapped back to the particles. This discretisation and interpolation of properties can lead to spurious entropy generation. In addition, particles in astrophysical structures tend to cluster into dense, compact objects. This generally leads most particles to reside on one or two blocks within the galaxy which typically lie on the same processor in large grid supercomputers. This creates very poor load balancing and increases communication overhead, spoiling the excellent scaling of massively parallel grid codes.

To resolve these problems, we have used the collisionless Boltzmann moment equations to generate a series of fluid equations which can be used to model  collisionless systems. We term this technique "collisionless stellar hydrodynamics" given the similarity it bears to conventional hydrodynamics. Using high resolution characteristic tracing MUSCL-Hancock schemes, we have implemented our collisionless stellar hydrodynamic approach into the massively parallel FLASH code. In doing so we remove all of the key disadvantages of the Particle-Mesh technique, allowing us to preserve the excellent scaling of the FLASH code and plan more ambitious future simulations. To read more about our colllisionless stellar hydrodynamic approach please see our paper:

Collisionless Stellar Hydrodynamics as an Efficient Alternative to N-Body Methods

Current applications include the development of a new truly multi-phase model of the ISM which allows the hot gaseous and cold molecular cloud phases to be modelled separately. This presents a significant advancement upon conventional single phase models which dominate and increases the amount of physics we can include without the need to resort to polytropic equations of state to approximate sub-grid physics.