Review of stokes flow past a sphere

Abstract

The slow viscous incompressible flow past a stationary sphere is studied. We review Stokes and Oseen approximations. The stream function approach is used to derive the solutions of incompressible fluid flow that were obtained by Stokes and Oseen. We solve the Stokes expansion using Mathematica and the code is given in the algorithms. The explicit finite difference method (FDM) is used to solve the fourth order differential equation that was derived from the full Navier-Stokes equations. We also investigate numerical solutions to the Stokes expansion using standard (FDM) in Mathematica. Using FDM iteratively we can find approximate solutions to higher moments in the stream function and compare these solutions with those found from the numerical solutions to the full Navier-Stokes equations.