2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/3442We summarize the ideas that led to the Adaptive Smoothed Particle Hydrodynamics (ASPH) algorithm, with anisotropic smoothing and shock-tracking. We then identify a serious new problem for SPH simulations with shocks and radiative cooling --- false cooling --- and discuss a possible solution based on the shock-tracking ability of ASPH.8 pages, 5 figures, to appear in Proceedings of IAU Symposium 208, Astrophysical Supercomputing Using Particles, eds. J. Makino and P. HutAstrophysicstext