Numerical study of Navier–Stokes equations

The problem of a viscous incompressible fluid flow around a body of revolution at incidence, which is described by Navier-Stokes equations, is considered. For low Reynolds numbers, the solutions of these equations are smooth functions. A numerical algorithm without saturation is constructed, which responds to solution smoothness. The calculations are performed on grids consisting of 900 (10 $\times$ 10 $\times$ 9) and 700 (10 $\times$ 10 $\times$ 7) nodes. On the grid consisting of 900 nodes, a system of 3600 nonlinear equations is solved by a standard code. The pressures on the shaded side of the body of revolution are compared. It is found that a numerical study (on this grid) is feasible for problems with $\mathrm{Re}\approx$ 1. For high Reynolds numbers, the number of grid nodes has to be increased.