Explore the fascinating world of astrophysical fluid dynamics in this comprehensive seminar presented by Professor James Stone from the School of Natural Sciences at the Institute for Advanced Study. Delve into various celestial phenomena, including the Sun, Jupiter's atmosphere, and the Carina nebula, while examining the mathematical models and numerical methods used to study them. Learn about ideal magnetohydrodynamics (MHD), MHD waves, and their phase velocities through Friedrichs diagrams. Discover cutting-edge computational techniques, such as finite-volume discretization, Godunov's method, and Adaptive Mesh Refinement (AMR), used to simulate and analyze complex astrophysical systems. Gain insights into the validation of physics modules and the importance of relativistic ray-tracing in future research.