Multgrid Lattice Boltzmann

I’m working on Multigrid with LBM, and I use A. Depuis formulation, Theory and applications of an alternative lattice Boltzmann grid refinement algorithm PHYSICAL REVIEW E 67, 066707 ~2003.following this algorithm, I make one collision and streaming step (including boundary conditions) in the coarse lattice, for the second step, after one collision-streaming step (without BC) I make a space interpolation using cubic Shema, and time interpolation using linear interpolation, for the distribution function, and I calculate feq directly from the interpolated distribution function to rescale PDF in the fine grid,but the resultats stil wrong. Can anyone help me on that.