An analysis and comparison of conservative upwind difference schemes for ideal and non-ideal gases

In a recent paper P. Glaister, Conservative upwind difference schemes for the Euler equations, Comput. Math. Appl. 45 (2003) 1673–1682] a number of numerical schemes were presented for the Euler equations governing compressible flows of an ideal gas, the principal one of which is based on a conservative linearisation approach. This scheme was subsequently extended to encompass compressible flows of real gases where the equation of state allows for non-ideal gases P. Glaister, Conservative upwind difference schemes for compressible flows of a real gas, Comput. Math. Appl. 48 (2004) 469–480]. These schemes use different parameter vectors in their construction and, consequently, the scheme in P. Glaister, Conservative upwind difference schemes for compressible flows of a real gas, Comput. Math. Appl. 48 (2004) 469–480] when applied to the special case of an ideal gas is not identical to the principal ideal gas scheme in P. Glaister, Conservative upwind difference schemes for the Euler equations, Comput. Math. Appl. 45 (2003) 1673–1682]. In this paper it is shown how these schemes are related, followed by a numerical comparison when each is applied to two standard test problems.