The study of the potential flow past a submerged hydrofoil by the complex boundary element method

We study the free-boundary linearized problem of the two-dimensional steady potential flow past a submerged hydrofoil. The integral representation obtained herein for the complex velocity involves only finite contours. The corresponding integral equation may be solved for any streamlined hydrofoil by means of the complex boundary element method. We calculate the free surface elevation, the velocity field, the pressure coefficients, the lift and the drag for the Kármán–Trefftz and Joukowsky hydrofoils and for the circular obstacle. A comparison between some numerical and analytical results shows a very good agreement.