Numerical Simulation of Incompressible 2D Laminar Flow and Pressure Field in Periodically Converging-Diverging Channels Using SIVA and SIMPLE Algorithms

In this study, the numerical solution of Navier-Stokes equations for two-dimensional parabolic flows is considered. The methods used are based on the SIVA (Simultaneous Variable Setting) and SIMPLE algorithms for the numerical solution of differential equations. Both methods follow different strategies in generating the flow field by solving the momentum and mass conservation equations. While the SIVA method provides solutions with simultaneous variable setting, the SIMPLE method is based on sequential approximations. These methods are solved with integral forms of differential equations in transformed coordinate systems and the velocity and pressure fields of the fluid are calculated. The analyses performed in shrinking–expanding channel geometries show that the secondary flows formed especially by the effect of the directors increase the pressure losses. The results reveal the changes in the velocity profiles depending on the Reynolds number and angle.