Convection diffusion with sinusoidal velocity

I solve the convection diffusion equation with a sinusoidal velocity as u = 1 + sin (2pi * t + phi)
How can I introduce the notion of time in my calculations
Thank you for your support

I think expression for sinusoidal velocity should be


u0 is the mean velocity. t is lattice time.
omega (=2*pi/T) is frequency and phi is small perturbation.

In LBM, u0<0.1.