Evaluate the Performance of the Scalar and Cusp Central Difference Schemes, AUSM+ Upwind Method in Very Low Mach Number up to Supersonic Flow

In recent years, achievement more accurate numerical method in different flow regimes for the discontinuities with less oscillation and numerical errors is the interest of many researchers. What distinguishes this paper is, comparison of the performance of artificial dissipation and upwind methods, in solving the Euler equations for internal compressible flows in a wide range of inlet Mach numbers. In this study we examined the ability of three AUSM upwind method, Scalar and Cusp artificial dissipation methodes from very low Mach up to ultrasound and non-viscous flow in a convergent-divergent nozzle. The ability of AUSM method and Scalar methods in two-dimensional inviscid sonic flow between turbine stator blades at both supersonic and subsonic outlet is also investigated. In this study an excellent performance for AUSM method with more convergence speed and low numerical error in all flow regimes at a converging-diverging nozzle is observed. In the second example, in both flow AUSM method presents the results based on experimental, with low numerical errors and satisfy the mass conservation better than Scalar. It should be mentioned that the AUSM method is highly recommended for higher Mach numbers.