Abstract
Analytical solutions and numerical solutions for the incompressible flow of a viscous fluid past a sphere are presented for a range of Reynolds number, Re, from Re=0.01 to Re=120. Flow patterns, drag and pressure distributions as predicted by analytical solutions to the Oseen equations of motion are compared with ones by numerical solutions to the Navier-Stokes equations of motion. In the range of low Reynolds numbers, they agree better with the ones by numerical solutions than the analytical predictions by the Proudman-Pearson method. But at intermediate Reynolds numbers, the analytical solutions for most properties deviate progressively from the numerical ones withRe. However, it should be noted that the qualitative nature of the flow field can be described by the Oseen solutions even at intermediate Reynolds numbers.
Lastly, successive approximations to the Navier-Stokes equations are carried out with the Oseen solutions ; the results for the first approximations up to Re=10 are useful for numerical solutions of the Navier-Stokes equations.
