  As the original velocity field obtained from four-dimensional (4D) flow
magnetic resonance imaging (MRI) contains considerable amount of noises and
errors, the available Divergence-free smoothing (DFS) method can be used to
process the 4D flow MRI data for reducing noises, eliminating errors, fixing
missing data and eventually providing the smoothed flow field. However, the
traditional DFS does not have the ability to deal with the flow in the near
wall region of vessel, especially for satisfying the no-slip boundary
condition. In this study, therefore, an improved DFS method with specific near
wall treatment is introduced for processing with 4D flow MRI inner flow with
curved wall boundary as the blood flows. On the other hand, due to the coarse
resolution of 4D flow MRI, velocity gradients in the near wall region are
normally underestimated. As a result, a special wall function is required for
accurately computing wall shear stress (WSS).
