We present entropy-limited hydrodynamics (ELH): a new approach for thecomputation of numerical fluxes arising in the discretization of hyperbolicequations in conservation form. ELH is based on the hybridisation of anunfiltered high-order scheme with the first-order Lax-Friedrichs method. Theactivation of the low-order part of the scheme is driven by a measure of thelocally generated entropy inspired by the artificial-viscosity method proposedby Guermond et al. Here, we present ELH in the context of high-orderfinite-differencing methods and of the equations of general-relativistichydrodynamics. We study the performance of ELH in a series of classicalastrophysical tests in general relativity involving isolated, rotating andnonrotating neutron stars, and including a case of gravitational collapse toblack hole. We present a detailed comparison of ELH with the fifth-ordermonotonicity preserving method MP5, one of the most common high-order schemescurrently employed in numerical-relativity simulations. We find that ELHachieves comparable and, in many of the cases studied here, better accuracythan more traditional methods at a fraction of the computational cost (up to 50% speedup). Given its accuracy and its simplicity of implementation, ELH is apromising framework for the development of new special- andgeneral-relativistic hydrodynamics codes well adapted for massively parallelsupercomputers.
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