The small intestine is a complex organ, whose inner walls are lined with a dense layer of micron-scale cylindrical or leaf-like structures, called the villi. The villi-wall layer significantly enhances the surface area for nutrient absorption in the gut. However, these structures also exhibit complex oscillatory motion, arising from the contractions of the smooth muscles in the gut walls, the purpose of which is not well understood. Inspired by the biological motility of the rat duodenum, we carry out simulations of simplified traveling contractions along the villi-wall of a symmetric 2D channel. The channel's geometric dimensions mimic rat duodenal physiology. We use the lattice Boltzmann method, with moving resolved villi boundaries, to compute the instantaneous and time-averaged flow in the channel. Each villus oscillates harmonically with frequency f and small amplitude a, maintaining a constant phase difference of ?f with its neighbors. We vary these parameters to explore regimes beyond the physiological conditions of duodenal flow. The instantaneous flow field reveals two distinct flow layers: one closer to the villi, termed the mixing layer, and another at the channel center, termed the advected layer. The mixing layer is dominated by oscillatory flow, where two asymmetric counter-rotating vortices travel along with the imposed wall contractions. The advected layer, on the other hand, is characterized by near-uniform, time-invariant flow. Surprisingly, the irreversible flow is opposite to the direction of the imposed wall-traveling contractions. We explain the mechanism of this counter-flow generation and map the evolution of the boundary between the flow layers, transitioning from a viscosity-dominated regime to an oscillatory inertia-dominated regime. Our results not only advance the understanding of nutrient flow and transport within the gut but also suggest a novel way for microfluidic flow control in confined channels.