Potential flow in a region with sharp change of boundary

摘要

A series solution is developed for the problem of potential flow in a region with sudden change of boundary. The boundary and continuity conditions are applied directly to the velocity potential; no ambiguities arise. The resulting linear equations for the amplitudes in the eigenfrequency expansion can be solved using the Gauss‐Seidel approximation method. This method allows the velocities to be computed accurately even near the transition region. Its convergence is closely connected with the physical properties of the solution. A simplified approximation for a river flowing into a harbor is the rectangular model given in the paper. In the course of applying Yeh’s method to this model for a comparison with experimental observations of the flow pattern, we discovered this extension of Yeh’s method.