In this paper the so-called slightly reduced Navier-Stokes (SRNS) equations with most streamwise viscous diffusion and heat conduction terms are investigated in detail. It is proved that the SRNS equations are hyperbolic-parabolic in mathematics, which is the same as the current RNS or PNS equations. The numerical methods for solving the RNS equations are, therefore, applicable to the present SRNS equations. It is further proved that the SRNS equations have a uniformly convergent solution with accuracy of 0 (ε2) or 0 (Re−1) which is higher than that of the RNS equations, and for a laminar flow past a flat plate the SRNS solution is regular at the point of separation and is a precise approximation to that of the complete Navier-Stokes equations. The numerical results demonstrate that the SRNS equations may give accurate picture of the flow and are an effective tool in analyzing complex flows.

Agarwal, R. K., 1981, “A Third-Order-Accurate Upwind Scheme for Navier-Stokes Solutions in Three Dimensions,” ASME/AIAA Conference on Computers in Flow Predictions and Fluid Dynamics Experiments, pp. 73–84.
Anderson, D. A., Tannehill, J. C., and Plether, R. H., 1984, Computational Fluid Mechanics and Heat Transfer, Hemisphere Publishing Corporation.
Courant, R., and Hilbert, D., 1962, Methods in Mathematical Physics, Vol. 2, Interscience.
Dean, W. R., 1950, “Note on the Motion of Liquid near a Position of Separation,” Proceedings of Cambridge Philosophical Society, Vol. 46.
Durst, F., Melling, A., and Writelaw, J. H., 1974, “Low Reynolds Number Flow over Plane Symmetric Sudden Expansion,” Journal of Fluid Mechanics, Vol. 64.
Gao, Z., 1988, “On the Simplified Navier-Stokes (SNS) Equations,” Science in China (Series A), No. 10.
Goldstein, S., 1948, “On Laminar Boundary-Layer Flow near a Position of Separation,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 1.
Kirtley, K. B., and Lakshminarayana, B., 1985, “Computation of Internal Incompressible Separated Flows Using a Space-Marching Technique,” AIAA Paper 85-1624.
Macagno, B. O., and Huang, T. K., 1967, “Computational and Experimental Study of a Captive Body,” Journal of Fluid Mechanics, Vol. 28.
Telionis, D. P., 1981, Unsteady Viscous Flow, Springer-Verlag.
This content is only available via PDF.
You do not currently have access to this content.