Numerical solution of the NavierStokes equations for 3D internal flows: An emerging capability
Abstract
The accuracy of 3D flow calculations is discussed. A good calculation procedure solves a set of finite difference equations reasonably quick. However, if the finite difference equations do not accurately reflect the governing differential equations, poor results will be obtained. For example, it is common practice in three dimensional flow calculations to use upwind differencing or more direct forms of numerical mixing to obtain well posed finite difference equations which are needed to maintain a stable calculation procedure. The erroneous numerical viscosity introduced can be of the same order as the natural laminar or laminar plus turbulent viscosities in the flows calculated. When numerical mixing is present a proper evaluation of viscosity or turbulence models cannot be made because the effects of numerical and physical mixing cannot be distinguished. A simple 2D example is used to demonstrate a practical method of obtaining the finite difference form of the convection term in momentum or other conservation equations. The 2D example introduces no numerical mixing, yet results in well posed, (i.e., strong center point coefficient) finite difference equations. The method consists of central differencing to eliminate numerical mixing and upwinded control volumes to obtain finite difference equations with strong point coefficients. An upwinding procedure for the control volumes which may be applied to three dimensional flow is given. Inviscid calculations of horseshoe vortex flow about a Rankine half body are presented.
 Publication:

In AGARD 3D Computation Tech. Appl. to Internal Flows in Propulsion Systems 24 p (SEE N8532293 2134
 Pub Date:
 May 1985
 Bibcode:
 1985ctai.agar.....S
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Inviscid Flow;
 Mixing;
 Three Dimensional Flow;
 Accuracy;
 Coefficients;
 Differential Equations;
 Efficiency;
 Momentum;
 Turbulence Models;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer