SPH Sod shock tube

What you are seeing: a one-dimensional smoothed-particle hydrodynamics (SPH) simulation of the Sod shock tube. The membrane at $x = 0.5$ separates a high-pressure left state ($\rho = 1$, $P = 1$, $v = 0$) from a low-pressure right state ($\rho = 0.125$, $P = 0.1$, $v = 0$). At $t = 0$ the membrane is removed.

The exact Riemann solution has three waves: a left-moving rarefaction fan (where the gas accelerates and rarefies), a contact discontinuity in the middle (where density jumps but pressure and velocity are smooth), and a right-moving shock (where density, pressure, and velocity all jump). The SPH method represents the fluid as 360 Lagrangian particles smoothed by a cubic-spline kernel; the artificial viscosity is what allows it to capture the shock.