This paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

本文涉及流体从二维管道流出并冲击无限楔形的情况。流体离开管道的地方，在流体和被动气体之间有一个自由表面。该模型是冲击平板的平面气泡和流动的概括。在没有重力和表面张力的情况下，可以得出精确的自由流线解。我们还构造了两个数值方案来计算包含表面张力和重力的解。第一种方法涉及将流映射到下半平面，在此推导仅涉及边界值的积分方程。该积分方程通过数值求解。第二种方法涉及将流域保形地映射到s平面中的单位磁盘上。然后将未知数表示为s。该系列被截断，并且系数通过数值求解。边界积分法的另一个优点是，它可以解决远场中的波动问题，这将在后面讨论。两种数值方法之间的良好一致性以及精确的自由流线解提供了对数值方案的检验。