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This paper presents an idealized morphodynamic model to predict river dune evolution. The flow field is solved in a vertical plane assuming hydrostatic pressure conditions. The sediment transport is computed using a Meyer-Peter-Muller type of equation, including gravitational bed slope effects and a critical bed shear stress. To avoid the necessity of modeling the complex flow inside the flow separation zone, we follow an approach similar to one used earlier to simulate the dynamics of wind-blown desert dunes. In case of flow separation, the separation streamline acts as an artificial bed and sediment avalanches down the leeside distributing evenly on the leeside at the angle of repose. Model results show that bed slope effects play a crucial role in the determination of the fastest-growing wavelength from a linear analysis. Flow separation is shown to be crucial to take into account if the dune lee exceeds a certain threshold slope. If flow separation is not included, dune shapes are incorrectly predicted and the dune height saturates at an early stage of bed form evolution, yielding an underprediction of dune height and time to equilibrium. The local bed slope at the dune crest plays a critical role for obtaining an equilibrium dune height. The simulation model is able to predict the main characteristics of dune evolution, such as dune asymmetry, dune growth, and saturation at a certain dune height. Dune dimensions, migration rates, and times to equilibrium compare reasonably well to various data sets.