We analyze, through numerical simulations, the single-phase liquid flow and associated passive scalar mixing in a tubular reactor that is agitated by lateral shaking, which induces the motion of a solid mixing element inside the reactor. The Reynolds number associated with the shaking motion is in the range 1200-5600. Dependent on its specific value, we perform direct or large eddy simulations. A fixed-grid lattice-Boltzmann method is used for solving the fluid flow. The moving boundary condition at the surface of the mixing element is dealt with by means of an immersed boundary method. To quantify mixing, a transport equation for a passive scalar is solved in conjunction with the flow dynamics.