An Accurate Second-Order Approximation Factorization Method for Time-Dependent Incompressible Navier-Stokes Equations in Spherical Polar Coordinates

A finite-difference method for solving three-dimensional, time-dependent incompressible Navier?Stokes equations in spherical polar coordinates is presented in detail. 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 tested by computing the spherical Couette flow between two concentric spheres with the inner one rotating. A comparison of the numerical solutions with available numerical results and experimental measurements is made. It is demonstrated that the numerical code is valid for solving three-dimensional, unsteady incompressible Navier?Stokes equations in spherical polar coordinates.

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