Higher Order Compact Scheme Combined with Multigrid Method for Momentum, Pressure Poisson and Energy Equations in Cylindrical Geometry

A higher-order compact scheme combined with the multigrid method is developed for solving Navier-Stokes equations along with pressure Poisson and energy equations in cylindrical polar coordinates. The convection terms in the momentum and energy equations are handled in an effective manner so as to get the fourth order accurate solutions for the flow past a circular cylinder. The superiority of the higher order compact scheme is clearly illustrated in comparison with upwind scheme and defect correction technique by taking a large domain. The developed scheme accurately captures pressure and velocity gradients on the surface when compared to other conventional methods. The pressure in the entire computational domain is computed and the corresponding fourth order accurate pressure fields are plotted. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results.