THE DEVELOPMENT OF A ONE‐STEP ACCURATE FLUX VECTOR‐SPLITTING IMPLICIT ALGORITHM FOR EULER AND NAVIER‐STOKES EQUATIONS

Abstract

This paper introduces a novel algorithm for solving the two‐dimensional Euler and Navier‐Stokes compressible equations using a one‐step effective flux vector‐splitting implicit method. The new approach makes a contribution by deriving a simple and yet effective implicit scheme which has the features of an exact factorization and avoids the solving of block‐diagonal system of equations. This results in a significant improvement in computational efficiency as compared to the standard Beam‐Warming and Steger implicit factored schemes. The current work has advantageous characteristics in the creation of higher order numerical implicit terms. The scheme is stable if we could select the correct values of the scalars (λ±ξ and λ±η) for the respective split flux‐vectors (F± and G±) along the ξ− and η−directions. A simple solving procedure is suggested with the discussion of the implicit boundary conditions, stability analysis, time‐step length and convergence criteria. This method is spatially second‐order accurate, fully conservative and implemented with general co‐ordinate transformations for treating complex geometries. Also, the scheme shows a good convergence rate and acceptable accuracy in capturing the shock waves. Results calculated from the program developed include transonic flows through convergence‐divergence nozzle and turbine cascade. Comparisons with other well‐documented experimental data are presented and their agreements are very promising. The extension of the algorithm to 3D simulation is straightforward and under way.

Citation

NG, E.Y.K. and LIU, S.Z. (1996), "THE DEVELOPMENT OF A ONE‐STEP ACCURATE FLUX VECTOR‐SPLITTING IMPLICIT ALGORITHM FOR EULER AND NAVIER‐STOKES EQUATIONS", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 6 No. 8, pp. 3-18. https://doi.org/10.1108/eb017554