An immersed interface method for flow past circular cylinder in the vicinity of a plane moving wall.

Two-dimensional flows past a stationary circular cylinder near a plane boundary are numerically simulated using an immersed interface method with second-order accuracy. Instead of a fixed wall, a moving wall with no-slip boundary is considered to avoid the complex involvement of the boundary layer and to focus only on the shear-free wall proximity effects for investigating the force dynamics and flow fields. To analyze the convergence and accuracy of our implementation, numerical studies have been first performed on a simple test problem of rotational flow, where the second order of convergence is confirmed through numerical experiments and an optimal range of relative grid-match ratio of Lagrangian to Eulerian grid sizes has been recommended. By comparing the force quantities and the Strouhal number, the accuracy of this method has been demonstrated on the flow past a stationary isolated cylinder. The cylinder is then put in proximity to the wall to investigate the shear-free wall proximity effects in the low Reynolds number regime (20≤ R e≤200). The gap ratio, e/ D, where e denotes the gap between the cylinder and the moving wall and D denotes the diameter of the cylinder, is taken from 0.10 to 2.00 to determine the critical gap ratio, ( e/ D) _{c r i t i c a l}, for the alternate vortex shedding, where the fluid forces, flow fields and the streamwise velocity profiles are studied. One of the key findings is that the ( e/ D) _{c r i t i c a l} for the alternate vortex shedding decreases as the Reynolds number increases. We also find that, in this low Reynolds number regime, the mean drag coefficient increases and peaks at e/ D = 0.5 with the increase of e/ D and keeps decreasing gently from e/ D = 0.5 to e/ D = 2.0, while the mean lift coefficient decreases monotonically with the increase of e/ D. New correlations are then proposed for computing force coefficients as a function of R e and e/ D for a cylinder in the vicinity of a moving plane wall. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]