On the numerical simulation of two-dimensional time-dependent flows of Oldroyd fluids. I: Basic method and preliminary results (Q1058376)

The author presents a finite difference method to solve the problem of time dependent flow of Oldroyd fluid past a circular cylinder. The equations are discretised using a cylindrical polar finite-difference grid with a transformation which has the effect of concentrating grid points near to the cylinder where variables change more rapidly. Twenty four grid points are used in the radial direction while sixty four in the angular direction. It is observed that for low elasticity the flow field is significantly different from the Newtonian case only initially, but as time goes on, the difference disappears, leaving streamlines which are only very slightly shifted downstream from the Newtonian streamlines. Drag coefficient is reported to be 13\% higher than the Newtonian drag. However, increased elasticity results in the form of an area of slow moving fluid around the cylinder which settles to a steady state.