Abteilung Astrophysik

Toro No. 2

This Riemann problem consists of two rarefactions and a stationary contact discontinuity. A lot of numerical schemes fail in this test because the state in the middle between the two rarefactions is close to vacuum which is difficult to handle numerically. Since the internal energy is obtained via division of pressure by density the errors in the internal energy are very large. The results become slightly better if the reconstruction is done in primitive variables instead of conservative variables.

(All physical quantities are given in dimensionless units.)

Initial conditions:

   left  right
 density Σ  1.0  1.0
 pressure P  0.4  0.4
 velocity v  -2.0  2.0

Parameters:

  heat capacity ratio γ  1.4
  Monocent parameter Θ  1.2
 Runtime T  0.12
 Resolution  100

Noh Problem