Comparison Results between MacCormack Scheme and Steger Warming Scheme for the Case of Supersonic Flow Pass through Divergent Nozzle

Abstract

The present work focuses on the development of computer code which allow the engine designer investigate the flow behavior through a divergent nozzle. The flow is assumed as quasi one dimensional and steady inviscid compressible flow. In other word the flow is governed by compressible Euler equation depending on the local Mach number. Solving such a mixed type of equation is difficult. The boundary between hyperbolic and elliptic region is not clear. To avoid such difficulty can be done through treating a steady flow problem as unsteady flow problems with the boundary condition is fixed with respect to time. As unsteady flow problem, the Euler equation becomes hyperbolic type of partial differential equation with respect to time. This approach allows one to solve the unsteady flow problem goes to a steady state solution. There are various methods can used for solving hyperbolic type of equation, such as MacCormacks scheme, Steger Warmings scheme, Beam Warmings Scheme and TVD Scheme. The present work used MacCormacks scheme and Steger Warming scheme will be used to investigate the flow behavior through a divergent nozzle. Comparison with analytic solution shows that Steger Warmings scheme gives a better result than MacCormacks scheme.