Convergence test of linear entropy wave. The horizontal axis N represents the number of grid points used in the x-direction. Shown are the L1 errors of the specific entropy (panel a), velocity component normal to the propagation direction of wave V_⊥ (panel b), mass density (panel c), and gas pressure (panel d). Each line corresponds to the form of RSST used in the simulation. The dashed line in each panel shows the analytical line of second-order convergence. Details of the test problem are given in Sect. 4.4.