  Based on IBUU simulations calibrated by previous efforts of the transport
model evaluation project, we have studied the specific shear viscosity $\eta/s$
of nuclear matter in the spinodal region using the Green-Kubo method. With the
momentum-independent mean-field potential which reproduces reasonably well
empirical nuclear matter properties and nuclear phase diagram, we have
generated dynamically stable and thermalized nuclear cluster systems in a box
with the periodic boundary condition. Extensive results of the $\eta/s$ at
different average densities and temperatures in uniform and non-uniform systems
are compared, and we found that the shear viscosity is smaller with nuclear
clusters due to the enhanced correlation of the energy-momentum tensor and the
stronger collision effect. The temperature dependence of the $\eta/s$ has a
minimum only at low average densities of $\rho<0.3\rho_0$. The present study
serves as a rigorous baseline calculation of the $\eta/s$ in nuclear systems
with clusters, and helps to understand the relation between the shear viscosity
and the nuclear phase diagram.
