A Comparison of Upwind Difference Schemes for Compressible Flows of Ideal and Non-Ideal Gases in a Duct.dvi

In a recent paper [1] a number of numerical schemes were presented for the Euler equations governing compressible flows of an ideal gas in a duct of variable cross section, the principal one of which is based on a conservative linearisation approach. This scheme was subsequently extended to encompass compressible duct flows of real gases where the equation of state allows for non-ideal gases [2]. These schemes use different parameter vectors in their construction and, consequently, the scheme in [2] when applied to the special case of an ideal gas is not identical to the principal ideal gas scheme in [1]. The schemes also vary as to whether the source term arising out of the geometry of the problem is handled using upwinding or treated as a point source. In this paper a numerical comparison of these schemes is made when each is applied to a standard test problem for the ideal gas case. Mathematics Subject Classification: 65M06, 35L65, 76L05