Abteilung Astrophysik

Sod Problem

This 1D Riemann problem first introduced by Sod has become a standard test case for compressible flow solvers. The test setup is quite simple: A tube is filled with two fluids separated by a thin membrane. The fluids are at rest on either side, but each fluid is initiallized with different density and pressure. Then the membrane is removed instantly leading to a discontinuous flow with all three types of non-linear waves. The test checks the ability of the numerical scheme to reproduce the Rankine-Hugoniot jump condition at the shock and the correct density profile in the rarefaction.

(All physical quantities are given in dimensionless units.)

Initial conditions:

   left  right
 density Σ  1.0  0.125
 pressure P  1.0  0.1
 velocity v  0.0  0.0


 heat capacity ratio γ  1.4
 Monocent parameter Θ  1.2
 Runtime T  0.25
 Resolution  100

Sod Problem