The application of splines to the numerical solution of the Navier-Stokes equations at high Reynolds numbers

The feasibility of using splines to approximate functions with large gradients in the case of the numerical solution of nonlinear problems is investigated. The example considered is the numerical solution of the Navier-Stokes equations for the flow of a viscous incompressible fluid past a flat semiinfinite plate at Reynolds numbers of 1000 to 100,000. It is shown that the use of splines on nonuniform grids makes it possible to achieve satisfactory results also for grids with a relatively small number of nodes.