Further development and additional details and tests of ASPH were presented by us in Owen et al. (1998, henceforth Paper II). As described above, the ASPH method replaces the isotropic smoothing algorithm of standard SPH, in which interpolation is performed with spherical kernels of radius given by a scalar smoothing length, with anisotropic smoothing involving ellipsoidal kernels and tensor smoothing lengths. Paper II presents an alternative formulation of the ASPH algorithm for evolving anisotropic smoothing kernels, in which the geometric approach of Paper I, based upon the Lagrangian deformation of ellipsoidal fluid elements surrounding each particle, is replaced by an approach involving a local transformation of coordinates to those in which the underlying anisotropic volume changes appear to be isotropic. Using this formulation the ASPH method is presented in 2D and 3D, including a number of details not previously included in Paper I, as well as advances or different choices with respect to Paper I. Among the advances included here are an asynchronous time-integration scheme with different time steps for different particles, a faster nearest-neighbor search algorithm, the stabilizing of kernel evolution by nearest-neighbor smoothing, and the generalization of the ASPH method to 3D. In the category of different choices, the shock-tracking algorithm described in Paper I for locally adapting the artificial viscosity to restrict viscous heating just to particles encountering shocks, is not included here. Instead, we adopt a different interpolation kernel for use with the artificial viscosity, which has the effect of spatially localizing effects of the artificial viscosity. This version of the ASPH method in 2D and 3D is then applied to a series of 1D, 2D, and 3D test problems, and the results are compared to those of standard SPH applied to the same problems. These include the problem of cosmological pancake collapse, the Riemann shock tube, cylindrical and spherical Sedov blast waves, the collision of two strong shocks, and problems involving shearing disks which demonstrate that ASPH has adequate angular momentum conservation properties. These results further support the idea that ASPH has significantly better resolving power than standard SPH for a wide range of problems, including that of cosmological structure formation.
This ASPH method tested favorably by comparison with many other cosmological gas dynamics codes when applied in 3D to the simulation of X-ray cluster formation in the so-called "Santa Barbara Cluster" comparison paper of C. Frenk et al. (1999). These latter ASPH simulations were run on a workstation and required only 32^3 particles each of gas and dark matter. Since then, our collaborator Owen (LLNL) has recently succeeded in parallelizing the ASPH method in 3D for any parallel computer which supports the newly established standard Open-MP parallel directives, so we are now ready to do 3D ASPH simulations of unprecedentedly large particle number and resolving power. In addition, Martel and Shapiro have now replaced the PM gravity solver used with our ASPH method, with a P3M gravity solver, to achieve higher spatial resolving power at fixed mass resolution.
| Previous page | Next page | Return to table of contents |