An HOC Based Immersed Interface Scheme for Uniform Flow Past a Circular Cylinder

In this paper, we develop a new HOC based immersed interface scheme in cylindrical polar coordinates for solving viscous, incompressible, laminar flow past a circular cylinder. This new scheme is developed by clubbing the recently developed higher order compact (HOC) methodology with with special interface treatment for the points just next to the points of discontinuity. Non uniform grid in polar coordinates (r, θ) is used for the discretization, where the surface of the cylinder is considered as an interface immersed in the fluid. Streamfunction-Vorticity formulation of Navier-Stokes equation in cylindrical polar coordinates is considered with an assumption that solution inside the immersed boundary is zero. Quantitative and qualitative results are shown for various values of Reynolds number Re ≤ 100 and an excellent agreement with existing numerical and experimental results is found in each case.