Abstract
A stable scheme for solving the Euler and Navier-Stokes compressible primitive variable equations by adding higher-order extra terms to the flux-vector splitting method has been developed. The approach eliminates approximate factorization and matrix operation. This gives an improvement in computational efficiency as compared to the standard Beam-Warming and Steger implicit factored schemes. The method is spatially second-order accurate, fully conservative and implemented with general coordinate transformations for treating the complex geometries. It shows good convergence rate and acceptable accuracy in capturing the shock waves. Results computed from the code include transonic flows through turbine stator, compressor rotor with large separate turbulent flow and supersonic compressor staggered wedge cascade. Comparisons with well-documented experimental data are included and the agreements are good.
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