In recent years, the lattice Boltzmann equation has developed into a promising technique for computational fluid dynamics (CFD). The lattice Boltzmann model (LBM) approach is derived from the Boltzmann equation and kinetic theory, as opposed to the standard CFD methods that are based on direct discretization of the Navier-Stokes equations. In this paper, Newtonian flow passing through a wavy walled channel has been examined for laminar to turbulent transition by using the LBM. The simple LBM for this problem becomes unstable as the Reynolds number increases and the laminar to turbulent transition begins. When Ehrenfest's limiters are introduced in the LBM, the simulation becomes stable for higher Reynolds numbers. Two types of channel geometries are studied here, the channel walls of relatively small amplitude and channel walls of large amplitude. Our findings are that for large amplitude channel walls, flow becomes unsteady for lower Reynolds numbers as compared to that for small amplitude channel walls. For large amplitude walls, the vortices formed exhibit periodic shedding inside the channel furrows and remain there. For small amplitude walls, the vortex shedding starts downstream of the channel. The present LBM variant is able to simulate small amplitude channel flow for a Reynolds number Re = 800 and large amplitude channel flow for a Reynolds number R = 570.