Flow Past a Circular Cylinder on a 2D Curved Surface Using Discrete Exterior Calculus*

We present results of flow past a circular cylinder embedded on a curved 2D surface using the approach of discrete exterior calculus (DEC) (Mohamed et al., Journal of Computational Physics, 312, 175-191, 2016). DEC has been demonstrated to exhibit good conservation of secondary flow quantities such as kinetic energy (for inviscid flows) and discretely satisfies vorticity conservation both locally and globally. Moreover, DEC is suitable for studying flows
over curved surfaces, because the discretization using DEC is independent of the coordinate system employed.  We consider two configurations: one in which the cylinder is embedded on a sphere (positive Gaussian curvature) and the other in which it is embedded on another cylinder (zero Gaussian curvature) at Reynolds number of 40 and 100.  We observe that key quantities of interest (drag coefficient, Strouhal frequency) for the present cases are comparable to those for the flow past a cylinder embedded on a flat surface suggesting a measure of robustness of such a flow when interpreted as an attractor of a nonlinear dynamical system.