Simulation trails improve accuracy and efficiency in astrophysical simulations

Computational fluid dynamics (CFD) simulation is a powerful tool for astrophysicists investigating cosmological phenomena such as star formation. It provides a basis for testing hypotheses concerning the physical processes occurring in space, where direct experimentation is not possible. Smoothed particle hydrodynamics¹ (SPH) is widely used for CFD simulations in astrophysics. A mesh-free approach, it simulates a set of representative particles as they evolve over time. Larger numbers of particles give more accurate results but at the cost of increased computation time. Also, as the particles get closer together the time step used must be decreased to maintain stability. The overall behavior, as shown in Figure 1, involves constraints that can be prohibitive for scientists working with personal computer hardware. Furthermore, since the particles move around, there is no guarantee that areas of interest will contain enough particles to be resolved well.

There are several approaches for tackling the computational complexity issues of SPH. Bate et al.² place particles in ‘bins’ according to the time step size that each requires, and advance them individually. This ensures the simulation advances at a sensible rate but does not address accuracy concerns. Kitsionas and Whitworth³ apply an automated splitting algorithm to particles to give a guaranteed resolution for the simulation and to ensure that physically based criteria are met. However, it can be hard to determine appropriate values for these criteria. We are working on a new approach called ‘simulation trails’⁴ that aims to increase both the accuracy and the efficiency of SPH simulations by allowing expert input into a simulation as it progresses.

Our approach, a form of computational steering, involves running the simulation twice: a low particle-count preview run followed by a high particle-count final run. The resolution for the first run is chosen such that the simulation advances quickly enough for interactive feedback. We allow users (experts in the domain) to indicate, on visualizations of the preview results, which regions of space they consider to be interesting. This selection, which may be varied as the simulation advances, forms a ‘trail’ in 3D space marking which areas are important and when. The trail is then followed at a higher resolution using more particles. At each time step, particles within the trail may be split if necessary to maintain a sufficient resolution in that region. Hence the higher resolution and associated higher computational costs are targeted only where and when they are required.

Our application also provides multiple-view visualizations of the current state of the simulation. The user can view isosurfaces, slices, and direct 3D views (see Figure 2) for any of the properties of the particles (density, temperature, chemical composition, etc.). Each of these views supports rotation, zooming, and filtering. Views can be linked so that changes to one view automatically affect the others to which it is linked. This is useful for exploring correlations between properties.

The resulting trail, consisting of areas of space and the periods of time during which they are interesting, is applied when the simulation runs for the second time with a much higher number of particles. The outcome is a set of results that has greater accuracy than a conventional SPH simulation (without splitting) but requires less computation time than results from other existing approaches that involve particle splitting. Figure 3 compares results from our new software with those from a conventional SPH simulation.

Simulation trails are a promising technique for improving the overall efficiency of SPH simulations. Our results show that better results can be obtained in less time by harnessing the knowledge of an expert user during the simulation process. Our next steps will be to apply this technique in detail to specific astrophysical problems and to investigate more intuitive ways of highlighting features and mapping trails.

Rick Walker is a PhD student in the Computing Laboratory at the University of Kent. He is working in the fields of visualization and computational steering. His current research interests deal with exploratory simulation.

Peter Kenny is a lecturer in computer science at the University of Kent with interests in scientific computing, computer graphics, and image processing. He earned his doctorate in physics from the University of York and has held posts at the Universities of York, Bradford, and Kent and with Plessey Research.

Jingqi Miao obtained her BSc (physics) and her MSc (theoretical physics) at Jiangxi Normal University in China and her PhD (theoretical physics) at Hull University in England. She worked as a postdoc in the Engineering Department at Queen Mary College, University of London, from 1998-2000, and as a postdoc in physics at Queen Mary College from 2000-2001. Since 2001, she has worked for the School of Physical Science at the University of Kent as a lecturer.