Significance of the Thin-Layer Navier—Stokes Approximation

Abstract

A versatile technique has evolved for formulating the governing equations for inviscid and viscous compressible flows. The Navier—Stokes equations are first written in Cartesian coordinates in divergence or conservation form. With an arbitrary time-dependent transformation of coordinates, Peyret and Viviand [388] have obtained a general conservation form of the Navier—Stokes equations in the computational coordinates. This approach has also been used to solve the Euler equations. In many cases the Navier—Stokes equations are simplified by retaining only the viscous terms with derivatives in the coordinate direction normal to the body surface. This is the thin-layer Navier—Stokes-equation approximation, with the initial development of these equations given by Steger [389]. The thin-layer approximation along with additional assumptions is also used in the parabolized Navier—Stokes solution procedure.