A Simulation Study on von Karman Vortex Shedding with Navier-Stokes and Shallow-Water Models

Abstract

This study aims to investigate the advantages of employing numerical models based on Shallow-water equations for simulating von Karman vortex shedding. Furthermore, a comparative analysis with Navier-Stokes equations will be conducted to assess their effectiveness. In addition to Reynolds number (Re), Froude number (Fr), relevant to water depth, plays an important role in the Shallow-Water modeling of the von Karman vortex. In this study, simulations of 2D von Karman vortex shedding are performed using the Navier-Stokes model and Shallow-Water model, employing the least-squares finite-element method for space discretization and θ-method for time integration. The computed vortices characteristics, including the recirculation zone behind the cylinder, vortices size, and frequency, are presented. In the Navier-Stokes modeling, the computed results indicate that the size of vortices in space decreases and the Strouhal number increases as Re increases. In the Shallow-Water modeling for the same Re condition, the size of vortices increases and the Strouhal number decreases as Fr increases.