Adaptive Smoothed Particle Hydrodynamics: Methodology. II.

Further development and additional details and tests of Adaptive Smoothed Particle Hydrodynamics (ASPH), the new version of Smoothed Particle Hydrodynamics (SPH) described in Shapiro et al. (1996; Paper I) are presented. 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. In standard SPH the smoothing length for each particle represents the spatial resolution scale in the vicinity of that particle, and is typically allowed to vary in space and time so as to reflect the local value of the mean interparticle spacing. This isotropic approach is not optimal, however, in the presence of strongly anisotropic volume changes such as occur naturally in a wide range of astrophysical flows, including gravitational collapse, cosmological structure formation, cloud-cloud collisions, and radiative shocks. In such cases, the local mean interparticle spacing varies not only in time and space, but in direction as well. This problem is remedied in ASPH, where each axis of the ellipsoidal