On the solution of the compressible Navier- Stokes equations using improved flux vector splitting methods

In this paper the accuracy of two flux vector splitting methods using upwind schemes up to the fourth order of accuracy for the solution of the unsteady compressible Navier-Stokes equations is improved. Two of the most well-known methods for the solution of the inviscid gas dynamic equations, the flux vector splitting method by Steger and Warming and the flux vector splitting method by van Leer are presented for the first time in combination with a five-point upwind scheme. Inaccuracies of flux vector splitting methods, which have been presented in the recent literature, can be eliminated using the present schemes in conjunction with proposed corrections for the flux splittings. The boundary layers can be approached with high-order accuracy. Investigation of the flux vector splitting method is also carried out in the context of a monotone upstream centered scheme for conservation law forms (MUSCL). The present techniques can be used in compressible viscous flows, predicting with accuracy viscous phenomena such as separation and shock boundary layer interaction. Fast convergence of the implicit method is obtained by solving the system of equations with the Gauss-Seidel relaxation technique. Investigation of the diffusion terms’ discretization scheme is presented.