On the integration of Riemann's compatibility condition in one-dimensional unsteady flow of a gas in thermodynamic equilibrium

Abstract

Riemann's compatibility condition, valid along the characteristics of a nonviscous, one-dimensional, unsteady flow of a gas in thermodynamic equilibrium is discussed. That part of it, that containes variables of state, is shown to be a path dependant integral. Its integration is carried out for flows, in which one variable of state remains constant. For multi-isentropic flow of a calorically perfect gas an ansatz is given, that approximates the path of integration of the Riemann condition as if the law of thermodynamic change along a characteristic were uniform for one step of the calculation.