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.