The result is a little off because of the mismatch in domain. I will fix it soon (also the Godunov method). Although the results look very similar to the Godunov method with exact Riemann solver, they are actually approximate state solver with HLLC scheme.

Red line is the solution given by Godunov method. Blue line is the exact Riemann problem solution. All discontinuities locate at x=0. W_L stands for initial primitive quantities (\rho,u,p) on the left side, W_R stands for initial primitive quantities (\rho,u,p) on the right side.

For each example, pictures on the left side are \rho vs x plot, pictures on the right side are u vs x plot

Example: Shock tube

Example: Two strong rarefaction

Example: Left rarefaction and right contact and shock wave

Example: Right half of Woodward and Colella problem

Example: Two shock case