A numerical study of nonspherical black hole accretion. II - Finite differencing and code calibration

A two-dimensional axisymmetric computer code for calculating fully relativistic ideal-gas hydrodynamics around a Kerr black hole is described. This code is being used to study fully dynamic inviscid-fluid accretion onto black holes, as well as the evolution and development of nonlinear instabilities in pressure-supported accretion disks. The numerical techniques are developed and discussed. A variety of alternate differencing schemes are compared on an analytic test bed. Some discussion is devoted to general issues in finite differencing. The working code is calibrated using analytically solvable accretion problems, including the radial accretion of dust and of fluid with pressure (Bondi accretion). Two-dimensional test problems include the spiraling infall of low-angular-momentum fluid, the formation of a pressure-supported torus, and the stable evolution of a torus.