Astrophysical Radiative Shock Simulations
We are undertaking very high resolution hydrodynamical simulations of hypersonic radiative wall shocks in 2 dimensions, using computed non-equilibrium cooling. A Mach 15-20 shockwave is propagated into media with density fluctuations with both power-law and gaussian spectra, and the development of the post shock thermal instabilities and turbulence is examined. We show that due to the intrinsic scales introduced by the cooling process, extremely high resolutions are required to achieve asymptotic solutions. The post shock turbulence is no longer a simple power-law, with strong dissipation occurring at intermediate scales. Finally, a fractal dimensional treatment of the resulting structures gives useful means of estimating the cooling efficiencies of these strong shocks compared to uniform or even steady models.
RFCD Codes240101, 240502, 240304
Significant Achievements, Anticipated Outcomes and Future Work
We are also addressing the numerical instability that arises in the directionally split computation of hydrodynamic flows when shock fronts are parallel to a grid plane. Transverse oscillations in pressure, density and temperature are produced that are exacerbated by thermal instability when cooling is present. We have developed a spatial oscillation filter method that removes stripes and permits other high velocity gradient regions of the flow to evolve in a physically acceptable manner. It also has the advantage of only acting on a small fraction of the cells in a two or three dimensional simulation compared to conventional methods, and does not significantly affect performance. These results were presented at the High Energy Density Laboratory Astrophysics 2002 conference in Ann Arbor (U. Michigan), and at workshops here in Australia and at the Lawrence Livermore National Laboratory, California.
The 2D inhomogeneous simulations have demonstrated the true resolution required for accurate modelling of thermal instabilities for the first time. When fully resolved, the fractal nature of the cooling plasma and the large fluctuations in density and pressure at many scales required extremely high resolution. The self-similar nature of the structures means that adaptive mesh techniques fail, and resort to the finest resolution over most of the grid. The implication of this is that fully 3D simulations, required to correctly simulate the internal turbulence of the post shock flows, will require approximately 10^(9-10) 3D grid cells. These 2D calculations on the VPP represent the preliminary tests for large scale calculations on the new APAC National Facility.
In the near future fully 3 dimensional simulations will be undertaken, with the aim of producing emission spectra that can be compared to observations of real astrophysical shockwaves.
Computational Techniques Used
Standard ways of dealing with this type of hydrodynamical problem include the introduction of artificial viscosity or grid "jittering". Artificial viscosity smoothes the shock over more than two zones, thereby reducing the fluctuations between zones parallel to the shock front. Grid-jittering involves displacement of the grid in an oscillatory fashion thereby smoothing fluctuations between cells in the additional grid resampling process. Both of these techniques can be useful. However, they have the disadvantage that they are applied to the entire flow. This has the consequence that otherwise sharp features, e.g. tangential discontinuities in velocity, are smoothed unnecessarily, degrading the resolution. We have developed a new approach involving a "localized oscillation filter". This filter applies a light smoothing to cells parallel to the shock front. However, the smoothing is restricted to cells local to the shock, thereby avoiding the undesirable side-effects of other methods.
We have utilized a version of the VH-1 code, made available by J. Blondin et al. via their website (http://wonka.physics.ncsu.edu/pub/VH-1/). We have extensively reorganized the basic code for vectorization and overall efficiency on the ANU Fujitsu VPP300 supercomputer as well as adding subroutines to update the energy density when optically thin radiative cooling is operating. The new code is now called, simply, ppmlr, to distinguish it from VH-1 and to refer to the method used.
The code achieved 98% vector efficiency, processing cells at up to 300,000 per second, and at the time this was the fastest available computing, which allowed the high resolution 2D models to be computed for the first time.
Publications, Awards and External Funding
ARC Large Grant: Jet-Cloud Interactions in Active Galactic Nuclei (related to v60 and the newer x34 project)
R. Sutherland, D. K. Bisset, G.V. Bicknell, The Numerical Simulation of Radiative Shocks I: The elimination of numerical shock instabilities using a localized oscillation filter, ApJ, 2002, submitted
R. Sutherland, G.V. Bicknell, The Numerical Simulation of Radiative Shocks II: 2D inhomogeneous radiative shocks, ApJ, 2002, in prep