Numerical studies of slow viscous rotating fluid past a sphere

Navier-Stokes equations for steady, viscous rotating fluid, rotating about the z-axis with angular velocity are linearized using Stokes approximation. The linearized Navier-Stokes equations governing the axisymmetric flow can be written as three coupled partial differential equations for the stream function, vorticity, and rotational velocity component. Only one parameter enters the resulting equations. The linearized equations are difficult to solve analytically and the method of matched asymptotic expansions is applied. Central differences are applied to the two-dimensional partial differential equations and are solved by the Peaceman-Rachford ADI method. The resulting algebraic equations are solved by successive over relaxation method.