7 Numerical Hydrodynamics on Null Cones

Numerical evolution of relativistic hydrodynamics has been traditionally carried out on spacelike Cauchy hypersurfaces. Although the Bondi–Sachs evolution algorithm can easily be extended to include matter [153], the advantage of a light cone approach for treating fluids is not as apparent as for a massless field whose physical characteristics lie on the light cone. However, results from recent studies of relativistic stars and of fluid sources moving in the vicinity of a black hole indicate that this approach can provide accurate simulations of astrophysical relevance such as supernova collapse to a black hole, mass accretion, and the production of gravitational waves.

 7.1 Spherically symmetric hydrodynamic codes
 7.2 Axisymmetric characteristic hydrodynamic simulations
 7.3 Three-dimensional characteristic hydrodynamic simulations
  7.3.1 Massive particle orbiting a black hole

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