Numerical studies of slow viscous rotating fluid past a sphere

Abstract

Navier-Stokes equations for steady, viscous rotating fluid, rotating about the zaxis with angular velocity ω 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 parameterR _eω =2ωa ²/v enters the resulting equations. Even the linearized equations are difficult to solve analytically and the method of matched asymptotic expansions is to be 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. Streamlines are plotted for Ψ=0·01, 0·05, and 0·25 andR _eω =0·1, 0·3, 0·5.