Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field toy model in 3+1D

Binary black hole simulations become increasingly computationally expensive with smaller mass ratios because the Courant-Friedrich-Lewy condition imposes smaller time steps by the need to resolve the smaller black hole. Here we propose and explore a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range (10−4?q?10−2), where purely perturbative methods may not be adequate. A region much larger than the small black hole is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. We apply this idea to a toy model of a scalar charge in a circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field in a 3+1D framework using SpECTRE, the new discontinuous Galerkin code of the SXS collaboration.