Herein, an efficient numerical method is presented to describe the flow of a liquid in an open channel with various types of bottom configurations. The method is developed for steady two-dimensional potential free surface flows. The resulting nonlinear problem is solved numerically by boundary integral equation methods. In addition weakly nonlinear solutions are derived. New solutions which complement those of Dias and Vanden-Broeck [J. Fluid Mech. 59, 93–102 (2004)] are presented. Furthermore some solutions for channel flows past dips in the bottom are discussed.
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