Comparative Study of Upwind and Averaging Schemes with Artificial Dissipation for Numerical Solution for Quasi-One-Dimensional Supersonic Flow

Abstract

In this study, a quasi-one-dimensional supersonic flow in a divergent nozzle has been numerically simulated. For this purpose, codes have been written in FORTRAN software. In this study, the finite-volume method has been used for simulation. Time discretization has been progressive. Consequently, the equations obtained are explicit. Characteristic equations are extracted for one-dimensional compressible flows. The gradient of all characteristic lines is positive. To calculate convective terms, both upwind and averaging methods have been used. Forth order dissipation have been used for averaging methods’ stability. The results of the two methods have been compared for the accuracy of the results and the convergence rate. The effect of artificial damping coefficient on the convergence rate and the accuracy of the results in the averaging method have been investigated. Independence of the network is also examined for both methods. The results of these two methods were compared with the results obtained from the exact method which was solved for one-dimensional isentropic flow. Results comparison illustrates that upstream method has a better accuracy and convergence speed.