Second-order accurate method with splitting of boundary conditions for solving the stationary axially symmetric Navier–Stokes problem in spherical gaps

A numerical method for solving the axisymmetric Dirichlet boundary value problem for the stationary incompressible Navier–Stokes system in spherical gaps is constructed by using the method of successive approximations and the second-order accurate finite-element implementation developed by the authors in the axisymmetric case for a fast converging iterative method with splitting of boundary conditions for the Stokes system in spherical gaps. Numerical experiments on exact solutions showed that the method is second-order accurate up to the axis of symmetry and the gap boundaries. A numerical study (on fine grids) is conducted to determine the convergence domain of the method, and its results are compared with available experimental data for spherical Couette flows driven by the rotation of a single sphere. The method proves to be highly efficient as applied to the computation of basic viscous incompressible flows in narrow spherical gaps.