Flow around a cylinder: Shallow-water modeling with diffusion-dispersion

The equations for two-dimensional (2D), horizontal flow are obtained by vertical depth-integration of the continuity and momentum equations. Diffusion-dispersion terms appear, containing turbulent and dispersion stresses. Turbulent stresses are expressed with the eddy-viscosity concept; dispersion stresses are evaluated using velocity distributions along and across the curved streamlines. The differential equations are solved using the MacCormack scheme. The numerical simulation was done for three runs; the expected alteration of the flow field around the cylinder is evident, notably the wake behind the cylinder. For comparison, two similar runs were performed in a laboratory channel. The velocity vectors upstream from the cylinder and along its sides are in reasonably good agreement. However, very close to the cylinder, the simulation sometimes underpredicts the velocities. Downstream from the cylinder, agreement is satisfactory both inside and outside the wake. The flow depths at the centerline both upstream and downstream from the cylinder are also in good agreement; however, along the cylinder circumference, the simulated flow depths are lower than the observed ones.