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

Abstract EN

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.