HLL Riemann Solver

We solved the Riemann problem for the Euler equations exactly, but many times in practice we use approximate Riemann solvers. The HLL solver is a popular solver. Research this method and implement it in the Euler code and compare the solutions you get with it to those with the exact solver.

A good place to start is in the paper The HLLC Riemann solver by E. F. Toro. That summarizes the HLL solver and the more accurate HLLC solver.