Author(s)

L. ˇSkerget & J. Ravnik

Abstract

Flow of an incompressible viscous fluid is considered. The velocity-vorticity formulation of the Navier–Stokes equations is used. The kinematics equation is solved for boundary vorticity values using the Boit-Savart law. Solution of the kinetics equation for the domain values is obtained by employing a macro element approach. Using macro elements enables simulations on dense meshes, since it substantially reduces the algorithm’s memory requirements. The developed numerical algorithm has been used to simulate laminar flow over a square cylinder in channel. Low Reynolds number steady state flow simulation as well as transient simulation at higher Reynolds numbers has been investigated. The results have been analysed in terms of velocity, vorticity and pressure field distributions in the wake of the cylinder. 1 Introduction Flows past bluff bodies are an interesting topic amongst engineers and researchers. A square cylinder is a basic example of such flows, its industrial applicability ranging from wind induced motion to turbulent sound generation. In general flows past bluff bodies exhibit complex phenomena such as separation, reattachment or vortex shedding. The numerical benchmark for laminar incompressible flow over a square cylinder was made by Breuer et al. [1] using lattice Boltzmann and finite volume methods. Recently turbulent flow over a square cylinder was considered by Sohankar [2] using the Large eddy simulation approach. Flow as well as heat transfer was considered by De and Dalal [3] for a study of a natural convection around a headed square cylinder in an enclosure. Ozgoren [4] studied experimentally the flow structure in the downstream of square and circular cylinders.

Keywords