Conservative upwind difference schemes for the Euler equations for real gas flows in a duct

Glaister, P. (2009) Conservative upwind difference schemes for the Euler equations for real gas flows in a duct. Computers & Mathematics with Applications, 57 (9). pp. 1432-1437. ISSN 0898-1221 doi: 10.1016/j.camwa.2009.01.028

Abstract/Summary

In a recent paper [P. Glaister, Conservative upwind difference schemes for compressible flows in a Duct, Comput. Math. Appl. 56 (2008) 1787–1796] numerical schemes based on a conservative linearisation are presented for the Euler equations governing compressible flows of an ideal gas in a duct of variable cross-section, and in [P. Glaister, Conservative upwind difference schemes for compressible flows of a real gas, Comput. Math. Appl. 48 (2004) 469–480] schemes based on this philosophy are presented for real gas flows with slab symmetry. In this paper we seek to extend these ideas to encompass compressible flows of real gases in a duct. This will incorporate the handling of additional terms arising out of the variable geometry and the non-ideal nature of the gas.