Solving Navier–Stokes equation for flow past cylinders using single-block structured and overset grids

Many complex fluid motions are driven by physical processes of instability, transition and turbulence dependent upon nonlinear mechanisms. Here, we solve the flow past cylinder(s) using single-block structured and overset grids by computing Navier–Stokes equation in two-dimensions. The suitability of a compact scheme in discretizing convection and diffusion terms are investigated first by looking at relevant numerical properties. Also, for the overset grid method, one of the methods is identified that shows the best results in minimizing interpolation error at sub-domain boundaries for an analytical test function. We provide extensive comparisons with experimental and other computational results for flow past a single cylinder, utilizing both single-block structured and Chimera or overset grids. Apart from showing instability of this flow calculated by these methods, we also compare the computed vorticity and velocity data using these two grids by employing the proper orthogonal decomposition (POD). We have analyzed and developed an overset grid method with compact scheme that does not need any filtering to control error. This has been ascertained by performing POD analysis. To show that the developed method is capable of handling complex geometries, we have computed flow past two cylinders in side-by-side arrangement. Results obtained capture the known flow characteristics for this arrangement well using relatively fewer number of grid points.