Direct numerical simulation on spherical couette flow based on a decoupling method with second-order accuracy in time and space

A finite-difference method for solving three-dimensional, time-dependent incompressible Navier-Stokes equations in spherical polar coordinates is presented. A new algorithm, which is second-order accurate in time and space, is considered, and decoupling between the velocity and the pressure is achieved by this algorithm. Further, the numerical method is used to simulate the spherical Couette flow between two concentric spheres with the inner one rotating. A comparison of the numerical results with the available experimental measurements was made. It is demonstrated that the numerical code is valid for solving three-dimensional, unsteady incompressible Navier-Stokes equations in spherical polar coordinates.