3.2.7 Example: expansion shock and rarefaction fan

Figure 30: Expansion shock (left) and - correct - rarefaction fan (right).

The Riemann problem in Fig. 30 should result in a rarefaction fan (right panel).

• Instead, the CIR scheme from Eq. (185) produces a stationary expansion shock that violates the entropy condition (172).
• The solution by the CIR scheme is stationary because its flux ($f=\frac{1}{2}$) is the same everywhere, even if the velocity ($v_{}=\pm 1$) changes sign.