Numerical study of a thin liquid film flowing down an inclined wavy plane

► Surface wave instabilities of flows along wavy surfaces with possibly rising bottom. ► Finite element ALE simulations of free-surface Navier-Stokes equations. ► Higher amplitude and shorter wavelength of bottom undulation stabilize the flow. ► Close agreement with theoretical results for infinitely long wavelengths. ► Excellent agreement on free surfaces based on shallow-water models.