Numerical simulation of the flow behind a circular cylinder subject to small-amplitude recti-linear oscillations

The problem of unsteady, laminar flow past a circular cylinder which performs recti-linear oscillations at an arbitrary angle η with respect to the oncoming uniform flow is considered. The flow is incompressible and two-dimensional, and the cylinder oscillations are harmonic. The motion is governed by the Navier-Stokes equations and the method of solution is based on the use of truncated Fourier series representations for the stream function and vorticity in the angular polar coordinate. A non-inertial coordinate transformation is used so that the grid mesh remains fixed relative to the accelerating cylinder. The Navier-Stokes equations are reduced to ordinary differential equations in the spatial variable and these sets of equations are solved by using finite difference methods, but with the boundary vorticity calculated using integral conditions rather than local finite-difference approximations. For comparison purposes the initial flow is determined at a high Reynolds number and is found to be in good agreement with a previous theoretical result.