  We study the relationship between granular development and magnetic field
evolution in the quiet Sun. 6 typical cases are displayed to exhibit
interaction between granules and magnetic elements, and we have obtained the
following results. (1) A granule develops centrosymmetrically when no magnetic
flux emerges within the granular cell. (2) A granule develops and splits
noncentrosymmetrically while flux emerges at an outer part of the granular
cell. (3) Magnetic flux emergence as a cluster of mixed polarities is detected
at the position of a granule as soon as the granule breaks up. (4) A dipole
emerges accompanying with the development of a granule, and the two elements of
the dipole root in the adjacent intergranular lanes and face each other across
the granule. Advected by the horizontal granular motion, the positive element
of the dipole then cancels with pre-existing negative flux. (5) Flux
cancellation also takes place between a positive element, which is advected by
granular flow, and its surrounding negative flux. (6) While magnetic flux
cancellation takes place at a granular cell, the granule shrinks and then
disappears. (7) Horizontal magnetic fields enhance at the places where dipoles
emerge and where opposite polarities cancel with each other, but only the
horizontal fields between the dipolar elements point orderly from the positive
element to the negative one. Our results reveal that granules and small-scale
magnetic flux influence each other. Granular flow advects magnetic flux, and
magnetic flux evolution suppresses granular development. There exist extremely
large Doppler blue-shifts at the site of one cancelling magnetic element. This
phenomenon may be caused by the upward flow produced by magnetic reconnection
below the photosphere.
