Simplified Navier-Stokes equations and combined solution of non-viscous and viscous boundary layer equations

Simplified Navier-Stokes equations and the combined solution of non-viscous and boundary layer equations are discussed. From the full Navier-Stokes equations and an analysis of the combined solution of non-viscous and boundary layer equations, simplified Navier-Stokes equations were worked out. A perturbation analysis which differs slightly from the match-perturbation-expansions of inner-outer layers developed by Van Dyke shows that the solution of the simplified Navier-Stokes equations are uniformly valid with accuracy of O(Re infinity (-1/2)) in the whole flow field, where Re infinity = P infinity U infinity L over Mu infinity, is the density of free stream, U infinity the x-component of velocity, L the characteristic length, and Mu infinity the dynamic viscosity of free stream.