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Effects of wall roughness/topography on flows in strongly confined (micro-)channels are studied by means of lattice Boltzmann simulations. Whereas wall roughness in macroscopic channels is considered to be relevant only for high-Reynolds-number turbulent flows (where the flow is turbulent even for smooth walls), it is shown in this paper that, in micro-channels, surface roughness may even modify qualitative features of the flow. In particular, a transition from laminar to unsteady flow is observed. It is found that this roughness-induced transition is strongly enhanced as the channel width is decreased. The reliability of our results is checked by computing the viscous shear stress and the Reynolds stress across the channel, their sum following the theoretical prediction for the stress balance perfectly. Furthermore, the solutions obtained obey the transformation rules of the Navier-Stokes equation: When expressed in reduced (dimensionless) units, results for various channel dimensions, forcing term or dynamic viscosity are identical provided that the channel shape and the Reynolds number are unchanged. The time evolution of the velocity fluctuations at the initial stages of the transition to flow instability is monitored. It is found that fluctuations first occur in the vicinity of the rough wall, supporting the interpretation of wall roughness as a source of fluctuations and thus flow instability. In addition to their physical significance, our results provide further evidence for the reliability of the lattice Boltzmann method in dealing with complex unsteady flows.