We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the Bernoulli equation. The Newton-like scheme is developed by employing shape derivatives in the weak forms, which allows us to update the position of the free surface and the potential on the free boundary by solving a boundary-value problem at each iteration. To validate the effectiveness of the approach, we apply the scheme to solve a problem involving the flow over a submerged triangular obstacle.

翻译：我们提出了一种形状-牛顿方法，用于求解一类通用自由边界问题，其中自由边界条件之一由伯努利方程控制。该牛顿类方法通过采用弱形式中的形状导数进行推导，从而能够在每次迭代中通过求解边值问题来更新自由表面的位置及自由边界上的势函数。为验证该方法的有效性，我们将此方案应用于求解绕流浸没三角形障碍物的问题。