  We evolve a scalar field in a fixed Kerr-Schild background geometry to test
simple $(3+1)$-dimensional algorithms for singularity excision. We compare both
centered and upwind schemes for handling the shift (advection) terms, as well
as different approaches for implementing the excision boundary conditions, for
both static and boosted black holes. By first determining the scalar field
evolution in a static frame with a $(1+1)$-dimensional code, we obtain the
solution to very high precision. This solution then provides a useful testbed
for simulations in full $(3+1)$ dimensions. We show that some algorithms which
are stable for non-boosted black holes become unstable when the boost velocity
becomes high.
