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Dam-break flows in general geometries with complex bed topography are simulated numerically using a high-resolution Godunov-type cut cell method. The model is based on the shallow water equations with appropriate source terms. A vertical step in the bed is treated efficiently and accurately with the surface gradient method. For dam-break flows occurring in complicated geometries, the Cartesian cut cell method together with transmissive boundary conditions is incorporated. Verification of the method is carried out by predicting dam-break flows typical of practical situations, i.e., dam-break flows over a vertical step into bent channels and a dam-break flow over a bump in a bed with both transmissive and reflective boundary conditions at the channel end. The results are compared with experimental data showing good agreement. The method is simple, efficient, and conservative. It shows promise for handling a …