2D Physical View
1D Eulerian Grid Density Profile
The Computational Challenge: When a star explodes, it creates a "shock front" where the plasma density jumps instantly from near-zero to extremely high (a square wave). In an explicit Eulerian grid, mathematical derivatives fail at these infinite cliffs.
The Fix & The Consequence: To keep the code stable, schemes like Lax-Friedrichs introduce Numerical Viscosity (diffusion). While this stops the simulation from crashing, notice how increasing the viscosity artificially "smears" the shockwave over time. The sharp ring of fire becomes a blurry, thick cloud, and the peak density drops drastically.