Conservative upwind differencing for isentropic flows

In a recent paper [1], a number of numerical schemes for the shallow water equations based on a conservative linearization were analysed. The current paper seeks to generalize this work to include the isentropic flow equations. This is an important first step in generalizing such schemes to encompass compressible flows of a real gas. Such flows are governed by the Euler equations with a nonideal equation of state as a general expression for the pressure. A similar expression for the pressure occurs in the isentropic flow equations.