  We propose a seamless multiscale method which approximates the macroscopic
behavior of the passive advection-diffusion equations with steady
incompressible velocity fields with multi-spatial scales. The method uses
decompositions of the velocity fields in the Fourier space, which are similar
to the decomposition in large eddy simulations. It also uses a hierarchy of
local domains with different resolutions as in multigrid methods. The effective
diffusivity from finer scale is used for the next coarser level computation and
this process is repeated up to the coarsest scale of interest. The grids are
only in local domains whose sizes decrease depending on the resolution level so
that the overall computational complexity increases linearly as the number of
different resolution grids increases. The method captures interactions between
finer and coarser scales but has to sacrifice some of the interaction between
the fine scales. The proposed method is numerically tested with 2D examples
including a successful approximation to a continuous spectrum flow.
