On the Slightly Reduced Navier-Stokes Equations

Abstract

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.