  A fourth-order finite volume embedded boundary (EB) method is presented for
the unsteady Stokes equations. The algorithm represents complex geometries on a
Cartesian grid using EB, employing a technique to mitigate the "small cut-cell"
problem without mesh modifications, cell merging, or state redistribution.
Spatial discretizations are based on a weighted least-squares technique that
has been extended to fourth-order operators and boundary conditions, including
an approximate projection to enforce the divergence-free constraint. Solutions
are advanced in time using a fourth-order additive implicit-explicit
Runge-Kutta method, with the viscous and source terms treated implicitly and
explicitly, respectively. Formal accuracy of the method is demonstrated with
several grid convergence studies, and results are shown for an application with
a complex bio-inspired material. The developed method achieves fourth-order
accuracy and is stable despite the pervasive small cells arising from complex
geometries.
