A paper in 12th Annual Conference of the CFD Society, Ottawa, Ontario, Canada, 9-12 May 2004 (The conference website http://www.cfd2004.org is no longer alive, check the last Internet Archive).
Authors: W. Asrar, Y. Wen Jiun, A. A. Omar, and M. K. Mawlood
Abstracts: Two higher-order compact finite difference approaches, the Hermitian and the Lax-Wendroff are examined by applying them to the subsonic-supersonic isentropic flow in a converging diverging nozzle. The governing equations for quasi-one dimensional inviscid flow in a nozzle are solved using the numerical algorithms developed by using the two fourth-order compact finite difference schemes along with a third-order strong stability preserving Runge-Kutta (SSPRK) time integration method. Results are obtained for steady state flow properties and the errors are computed by using exact solutions. With the current formulation, the Hermitian scheme converges well while the Lax-Wendroff scheme does not provide good results.
Full paper can be downloaded from here.