Fig. 1. Evolutionary curves of perturbation under supersonic condition: (a) Initial perturbation values and initial conditions (I); (b) initial perturbation values and initial conditions (II).

Fig. 2. Evolutionary curves of perturbation under subsonic condition: (a) Initial perturbation values and initial conditions (III); (b) initial perturbation values and initial conditions (IV).

Fig. 3. Evolutionary curves of perturbation in transverse direction: (a) Initial perturbation values (V); (b) initial perturbation values (VI); (c) initial perturbation values (VII); (d) initial perturbation values (VIII).

Fig. 4. Density contours for 2D Sedov blast wave problem: (a) HLLEM; (b) x-HLLE+y-HLLEM (c) x-HLLEM+y-HLLE.

Fig. 5. Curves for three different shock-detecting functions.

Fig. 6. Density contours of random numerical noise problem: (a) HLLEM; (b) M-HLLEM-g; (c) M-HLLEM-g₁; (d) M-HLLEM-g₂.

Fig. 7. Maximum magnitude of velocity in y-direction of random numerical noise problem.

Fig. 8. Density contours of hypersonic flow over a cylinder: (a) HLLEM; (b) M-HLLEM.

Fig. 9. Density contours of double Mach reflection problem: (a) HLLEM; (b) M-HLLEM.

Fig. 10. Pressure contours of 2D Sedov blast wave problem: (a) HLLEM; (b) M-HLLEM.

Fig. 11. Density distribution of 2D inviscid contact discontinuity problem.