An Application of Homotopy Analysis to the Viscous Flow Past a Circular Cylinder

We consider the application of a new analytic method based on homotopy analysis to the solution of the steady flow of a viscous incompressible fluid past a fixed circular cylinder. The solutions obtained using this method produce some interesting results. For instance, an analytic verification of the critical Reynolds number Rd for which a standing vortex first appears behind the cylinder is given for the first time and found to be Rd 2.4. Since these values of the critical Reynolds number are beyond the range of validity of Oseen theory, no analytic verification of this value had previously been given. As a check on the accuracy of the solutions, the calculated drag coefficients at 6th-order approximation are found to agree reasonably well with experimental measurements for Rd 30 which is considerably larger than the Rd 1 results currently available using other analytic techniques. This buttresses the usefulness of the homotopy analysis method HAM as an important tool in solving highly nonlinear problems.