A form of the supersonic flow equations for an ideal gas

Abstract

Non-linear partial differential equations that govern the steady supersonic three-dimensional flow of an inviscid ideal gas with constant specific heats in an arbitrary curvilinear co-ordinate space are derived. A special form of these equations is constructed for the case when two families of stream surfaces and one family of parallel planes are used as co-ordinates. Characteristic equations equivalent to this special form are obtained. The characteristic equations are suitable for numerical integration of the equations of motion to obtain solutions of mixed initial and boundary value problems. The characteristic equations are a generalized form of similar equations used by Walkden and Caine as the basis of a numerical method of calculating supersonic two-dimensional and axi-symmetric flow fields.