A numerical testbed for singularity excision in moving black hole spacetimes

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.