Macroscopic phenomena in nature - in astrophysics and on Earth - often originate from the interaction of tightly coupled microscopic processes with different characteristic length and time scales. We develop efficient transport/hydrodynamics algorithms in the context of gravitational collapse and supernova explosions. A reliable numerical link between the input physics and the observables in distant astrophysical objects provides new information about matter under otherwise inaccessible conditions, or vice versa, allows the prediction of a large-scale evolution based on well-known input physics.