On a flow around a cylinder over uneven bottom

A plane problem of a potential fluid flow around a cylinder of arbitrary section over an uneven bottom with a flow velocity at infinity directed parallel to the bottom is considered. The circulation of the velocity field is determined from Goldshtik’s postulate: the maximum velocity on the contour of the cylinder must be minimal. Two numerical schemes of the boundary element method are developed for solving this problem. The first scheme determines the flow on a bounded but arbitrarily defined bottom surface. The second scheme determines the flow around a contour in a half plane. The comparison of calculations using these numerical schemes with the exact solutions shows the convergence of the method as the grid elements increase. The pressure on the cylinder surface and on the bottom obtained using numerical calculations by the $k$–$\omega$ model is compared with experimental data. Streamlines are also compared taking into account the separation region.