  An Integral Equation (IE) based field solver to compute the scattered fields
from spatially dispersive metasurfaces is proposed and numerically confirmed
using various examples involving physical unit cells. The work is a
continuation of [1], which proposed the basic methodology of representing
spatially dispersive metasurface structure in the spatial frequency domain,
$\boldsymbol{k}$. By representing the angular dependence of the surface
susceptibilities in $\boldsymbol{k}$ as a ratio of two polynomials, the
standard Generalized Sheet Transition Conditions (GSTCs) have been extended to
include the spatial derivatives of both the difference and average fields
around the metasurface. These extended boundary conditions are successfully
integrated here into a standard IE-GSTC solver, which leads to the new
IE-GSTC-SD simulation framework presented here. The proposed IE-GSTC-SD
platform is applied to various uniform metasurfaces, including a practical
short conducting wire unit cell, as a representative practical example, for
various cases of finite-sized flat and curvilinear surfaces. In all cases,
computed field distributions are successfully validated, either against the
semi-analytical Fourier decomposition method or the brute-force full-wave
simulation of volumetric metasurfaces in the commercial Ansys FEM-HFSS
simulator.
