Some theoretical aspects of the simplified Navier-Stokes(SNS) equations

Abstract

This study deals with the formulation, mathematical property and physical meaning ofthe simplified Navier-Stokes (SNS) equations. The tensorial SNS equations proposed is thesimplest in form and is applicable to flow fields with arbitrary body boundaries. The zonesof influence and dependence of the SNS equations, which are of primary importance to nu-merical solutions, are expounded for the first time from the viewpoint of subcharacteristics.Besides, a detailed analysis of the diffusion process in flow fields shows that the diffusioneffect has an influence zone globally windward and an upwind propagation greatly depressedby convection. The maximum upwind influential distance of the viscous effect and the rela-tive importance of the viscous effect in the flow direction to that in the direction normal tothe flow are represented by the Reynolds number, which illustrates the conversion of thecomplete Navier-Stokes (NS) equations to the SNS equations for flows with large Reynoldsnumber.