Computational advances and challenges in simulations of turbulence and star formation

Abstract We review recent advances in the numerical modeling of turbulent flows and star formation. An overview of the most widely used simulation codes and their core capabilities is provided. We then examine methods for achieving the highest-resolution magnetohydrodynamical turbulence simulations to date, highlighting challenges related to numerical viscosity and resistivity. State-of-the-art approaches to modeling gravity and star formation are discussed in detail, including implementations of star particles and feedback from jets, winds, heating, ionization, and supernovae. We review the latest techniques for radiation hydrodynamics, including ray tracing, Monte Carlo, and moment methods, with comparisons between the flux-limited diffusion, moment-1, and variable Eddington tensor methods. The final chapter summarizes advances in cosmic-ray transport schemes, emphasizing their growing importance for connecting small-scale star formation physics with galaxy-scale evolution.