  In this paper, we propose a numerical scheme to solve the kinetic model for
chemotaxis phenomena. Formally, this scheme is shown to be uniformly stable
with respect to the small parameter, consistent with the fluid-diffusion limit
(Keller-Segel model). Our approach is based on the micro-macro decomposition
which leads to an equivalent formulation of the kinetic model that couples a
kinetic equation with macroscopic ones. This method is validated with various
test cases and compared to other standard methods.
