A thirdorderaccurate upwind scheme for NavierStokes solutions in three dimensions
Abstract
A finitedifference method, accurate and stable at high Reynolds numbers, is described for the numerical solution of the steady NavierStokes equations in three dimensions. The basic governing equations are expressed in terms of three equations for the velocity components and three equations for the vorticity components. The equations for the velocity components are of Poisson type and are differenced using the conventional threepoint central differences. Convective terms in the transport equations for the vorticity components are differenced using a thirdorderaccurate upwind scheme. Difference equations thus obtained are solved by an alternating direction, lineiterative algorithm. Numerical results are presented for flow inside a cubic box resulting from the motion of one of its sides moving parallel to itself for Reynolds numbers up to 400. Comparison is made with the computations of other investigators based on the secondorder methods. A thorough documentation of the flow structure for this important model problem is provided.
 Publication:

In: Computers in flow predictions and fluid dynamics experiments; Proceedings of the Winter Annual Meeting
 Pub Date:
 1981
 Bibcode:
 1981cflp.proc...73A
 Keywords:

 Error Analysis;
 Finite Difference Theory;
 NavierStokes Equation;
 Numerical Stability;
 Three Dimensional Flow;
 Upstream;
 Boltzmann Transport Equation;
 Computational Fluid Dynamics;
 Convective Flow;
 Flow Geometry;
 Reynolds Number;
 Vorticity;
 Fluid Mechanics and Heat Transfer